0 |

0-diagonally convex relation |

3D-2D dimension reduction |

\delta)- pseudomonotone-type |

$\emph{p}$-Laplacian |

(\eta |

$\Gamma$-convergence |

$\phi$-monotone operators |

\theta |

$\varphi$--monotone subdifferential of order two |

A |

a priori bound |

absolute stability |

absolutely continuous |

absolutely continuous map |

abstract function spaces |

abstract space |

abstract Volterra integro-differential equations |

accretive operator |

acute cone |

acyclic multifunction |

adjoint equation |

admissible map |

admissible mappings |

admissible set |

advanced argument |

almost periodic functions |

analytic semigroups |

analyticity of semigroups |

anisotropic Sobolev spaces |

anti-periodic |

anti-periodic solution |

approximatable function |

approximatable set-valued map |

approximate controllability |

arcwise connectedness |

asymptotic behavior |

asymptotic center |

Asymptotic estimates |

asymptotic stability |

attractivity |

Aumann integrals |

Aumann's integral |

automatic differentiation |

averaging method |

averaging principle |

B |

Baire classification |

ball intersections |

Banach algebras |

Banach spaces |

Banach's contraction principle |

bang-bang principle |

base normed spaces |

best approximation |

blow up time |

Bohnenblust-Karlin's fixed point |

Borsuk-Ulam theorem |

boundary integral equation |

boundary value problem |

bounded $\varphi$-variation in the sense of Hardy-Vitali-Tonelli |

Bregman function |

Browder-Fan fixed point |

Browder-Minty theorem |

bulk and surface |

bundle method |

BV solution |

C |

$C_0$ semigroups |

$C_{0}$-{\it semigroup} |

$c_{0}$-semigroups |

$C_0$-semigroups |

C_0-semigroups |

caputo fractional derivative |

Caputo fractional derivative |

Caputo fractional order derivative |

Caputo-Hadamard fractional boundary value problem |

Carathéodory conditions |

categories of Lipschitz spaces |

Cauchy method |

Cauchy problem |

causal mappings |

central stretching |

Cerami condition |

characteristic equation |

Chebyshev approximation |

Clarke subdifferential |

closed and locally expansive mappings |

coercive map |

coercive operator |

coincidence |

coincidence points |

coincidence theorem |

common Lyapunov function |

commutator |

compact |

compact embedding |

compact operator |

compactness |

complementarity |

complemented subspace |

completion |

complex variable |

condensing map |

condensing multimap |

condensing multivalued map |

condensing operator |

conditional expectation |

contingent derivative |

continuous dependence |

continuous dependence of solutions |

continuous function |

continuous operators |

continuous selection |

continuous semimartingals |

continuous solution |

contracting mapping |

contractive type set-valued operators |

control of PDE |

control system |

controlability |

controllability |

convergence property |

convex |

convex and nonconvex problem |

convex feasibility problem |

convex minimization |

convex multivalued map |

convex nondi erentiable minimization |

convex nondifferentiable minimization |

convex optimization |

convex programming |

convex sets |

convexity |

cosine series |

cost functional |

critical point |

critical points |

curvilinear hole |

cylindrical controllability |

cylindrical mild solution |

D |

dealy |

decomposability |

decomposable hull |

decomposable set |

delay |

delta differential games |

demiclosed graph |

demicontinuous operator |

derivo-periodic multivalued functions |

deterministic |

difference inclusion |

difference inclusions |

differential equations |

differential equations in abstract spaces |

differential inclusion |

differential inclusions |

differential of multivalued functions |

direct optimization methods |

Dirichlet boundary condition |

Dirichlet boundary controls |

Diriclet boundary conditions |

discrete inclusion |

discrete-time switched systems |

distributed control |

distributed parameter systems |

double sine-cosine series |

dual dynamic programming |

dual form of KKM principle |

dynamic games on time scales. |

dynamic models |

dynamic unilateral problem |

E |

effective energy integral functional |

Ekeland's variational principle |

elastic membranes |

elliptic equations |

elliptic-parabolic equation |

energy |

entropy solution |

entropy solutions |

equilibrium points |

equilibrium states of the film |

Erd\'elyi-Kober fractional operator |

error estimates |

Esclangon's technique |

evolution |

evolution differential inclusion |

evolution inclusion |

evolution problem |

evolution triple |

existence |

existence, fixed point |

existence of optimal controls |

existence of optimal drift-diffusion-jump triples |

existence of optimal operators in the presence of uncertainty |

existence of solution |

existence of solutions |

existence result |

existence results |

existence theorem |

exponential stability |

extended Mangasarian-Fromovitz constraint qualification |

extension spaces |

extremal solution |

extremal trajectory |

extremals |

F |

Fan-Glicksberg fixed point and best approximation |

Fan-type element |

f-approximatively compact |

feedback operators |

Fejér monotone iterative methods |

Fejer monotone mappings |

fibering method |

Fillipov's selection theorem |

finite dimensional operators |

finite element approximations |

finitely additive measure solutions |

fixed point |

fixed point theorem |

fixed point theorem and differential inclusion |

fixed point theorem and integral inclusion |

fixed point theorems |

fixed points |

fixed points set |

forward mode |

Fourier boundary conditions |

Fourier transforms |

fractional $p$-Laplace equation |

fractional $p$-Laplacian |

fractional calculus |

fractional cosine family |

fractional differential equation |

fractional differential equations |

fractional differential inclusion |

fractional differential inclusions |

fractional integral |

fractional integro-differential equation |

fractional integro-differential inclusions |

fractional order |

fractional order differential equations |

fractional Sobolev space |

fractional stochastic differential equations |

Frechet space |

Fréchet space |

Fr\'echet spaces |

Fréchet subdifferential |

function increasing with respect to each variable |

functional differential inclusion |

functional integral equation |

functional-integral equation |

fundamental solution |

fuzzy metric spaces |

fuzzy random variable. |

fuzzy stochastic process |

fxed point theorem |

G |

gelfand triple |

generalised metric KKM mapping |

generalized monotonicity |

generalized Newton methods |

generalized random Lipschitzian mapping |

generalized second-order directional derivative |

generalized strongly nonlinear implicit variational inequality |

Generating spaces of quasi-metric family |

Ginzburg-Landau equation |

global attractor |

global optimization |

Górniewicz-type fixed point theorem |

guiding function |

H |

Hadamard fractional derivative |

Hadamard partial fractional integral |

Hadamard-type fractional calculus |

half-line |

Hammerstein integral equation |

Hausdorff dimension |

Hausdorff-Pompeiu generalized semi-metric |

hemicontinuity |

hemivariational inequalities |

hemivariational inequality |

Henstock-Kurzweil integral |

Henstock-Kurzweil-Pettis integrals |

Hilbert space |

Hilbert spaces |

Hilfer and Hadamrd fractional derivatives |

history |

HJB equation |

homogeneous Neumann boundary condition |

Hukuchara's derivative |

hybrid differential inclusions |

hyperbolic differential inclusion |

hyperbolic equation |

hyperconvex space |

I |

identification |

implicit fractional differential inclusion |

impulsiv einclusion |

impulsive |

impulsive controls |

impulsive fractional differential inclusions |

impulsive functional differential inclusion |

impulsive initial value problem |

impulsive perturbations |

impulsive systems |

indefinite potential |

induced measure valued functions |

infinite delay |

infinite dimension |

infinite plate |

initial value problems |

input-to-state stability |

integrably boundedness of set-valued integral |

integral boundary conditions |

integral equations |

integral guiding function |

integral inclusion |

integral method |

integral solution |

integration by parts |

integrodifferential equation |

integro-differential equations |

integrodifferential equations |

integrodifferential evolution equations |

interior point methods |

invariance |

invariant measure |

invariant subspaces |

inverse mappings |

inverse operator method |

inverse problem |

isomorphic spaces |

iteration |

iterative method |

It\^o set-valued integral |

J |

j-bounded space |

j-contractive mapping |

jointly upward functions |

K |

KKM mapping |

KKM property minimax theorem |

Krasnoselsk'ii's fixed point theorem |

Kuratowski measure of noncompactness |

Ky Fan matching theorem |

L |

Lagrange function |

Langevin equation |

large scale optimization |

Lefschetz spaces |

left-sided mixed Riemann-Li\-ouville integral |

left-sided mixed Riemann-Liouville integral |

left-sided mixed Riemann-Liouville integral of fractional order |

Leray-Schauder alternative |

Leray-Schauder alternative theorem |

Leray-Schauder degree |

Leray-Schauder nonlinear alternative principle |

Leray-Schauder principle |

level control |

level set |

level set method |

L\'evy-Prohorov metric |

L-generalized pseudomonotonicity |

linear feasibility |

linear functional equation |

linear quadratic optimal control problems |

linearity of contingent derivative |

linear-quadratic control for Volterra integral systems |

Liouville equation |

Lipschitz |

Lipschitz continuity |

Lipschitz functions |

Lipschitz property |

Lipschitz selections |

Lipschitzean |

local intersection property |

locally selectionable multifunction |

long steps |

lower solution |

Lyapunov function |

M |

m-accretive operator |

malaria dynamics |

mapping method |

Marcinkiewicz spaces |

marginal value function |

martingales |

mathematical modeling |

mathematical programming |

matrix equations |

maximal monotone graph |

maximal monotone map |

maximal monotone operator |

Maximal monotone operator |

maximal monotonicity |

maximum function |

McKean-Vlasov stochastic differential equation |

mean |

measurability of multifunctions |

measurable selection |

measurable selectors |

measurable vector fields |

measure of non-compactness |

measure of noncompactness |

measure of weak non-compactness |

measure of weak noncompactness |

measure solutions |

measures of noncompactness |

measures of weak noncompactness |

Meir-Keeler type mapping |

method of upper and lower solutions |

metric space |

mild solution |

mild solutions |

minimal points |

minimax theorems |

minimizers of variational integral functionals |

min-max |

M\"{o}nch fixed-point theorem |

monotone operator |

monotone operators |

Monte Carlo method |

mountain pass theorem |

multidimensional control problems |

multifunctions |

multivalued compact operators |

multivalued differential |

multivalued map |

multivalued mapping |

multi-valued operator |

N |

necessary condition of optimality |

necessary conditions |

necessary conditions of optimality |

necessary optimality condition |

necessary optimality conditions |

Nemytski operator |

Neumann boundary |

neutral differential equations |

neutral equation |

neutral stochastic functional differential equation |

neutral type |

neutral type systems |

Nikaidô's coincidence theorem |

non-causal feedback |

noncompact Lipschitzean right-hand side |

nonconvex |

nonconvex sweeping process |

nonhomogeneous equations |

nonlinear |

nonlinear abstract inclusion |

nonlinear boundary conditions |

nonlinear degenerate parabolic problem |

nonlinear elliptic |

nonlinear mapping |

nonlinear nonautonomous systems |

nonlinear optimization |

nonlinear recurrence of second order |

nonlinear semigroup |

nonlinear stochastic systems |

nonlinear systems |

nonlocal boundary conditions |

nonlocal Cauchy problem |

nonlocal condition |

nonlocal initial condition |

non-local problem |

non-polyhedral set |

non-power-growth-type bulk energy density |

nonreflexive Banach spaces |

nonseparable $C(K)$ spaces |

non-slfadjoint operators |

non-smooth critical point theory |

nonsmooth functions |

non-smooth guiding function |

nonstandard Riccati equations |

norm estimates |

normal cone |

normal structure |

not instantaneous impulses |

numerical |

O |

objective functionals |

obtuse cone |

obtuse cone selection |

one sided Lipschitz multifunctions |

open |

operator differential inclusion |

operator measures |

operator valued functions |

optimal control |

optimal control of measures |

optimal control problem |

optimal controls |

optimal feedback control |

optimal feedback controls |

optimal flow rate |

optimal shape design |

optimality conditions |

optimization |

optimization method |

order interval |

ordered space |

ordinary differential inclusions |

oscillation |

oscillation theorems |

oscillation theory |

oscillatory solution |

Oshman space |

P |

Palais-Smale condition |

parabolic system |

parametric projection |

parbolic equation |

partial difference equations |

partial functional integrodifferential equations with state-dependent delay |

partially closed graph |

partially observed |

partition of unity |

$p(\cdot)$-capacity |

penalty function |

penalty/barrier |

periodic multivalued functions |

periodic problem |

periodic solution |

perturbation |

perturbations |

Pettis integral |

Pettis integrals |

p-factor operator |

phase space |

piecewise lower (upper) semi-continuous |

Poisson jumps |

Pontryagin Maximum Principle |

Pontryagin's Maximum Principle |

positive coefficients |

positive solution |

positive solutions |

p-regularity |

primal dual algorithm |

probabilistic metric spaces |

projection methods |

projection onto convex sets |

proper orthogonal decomposition |

property (B) |

proximal algorithm |

proximal point algorithm |

pseudo-distance |

Pseudometrically convex uniform space |

pseudomonotone operator |

pseudo-solutions |

p-uniformly convex Banach space |

$p(x)$-Laplacian |

Q |

$q$-difference inclusions |

quadcopter |

quadratic integral equation |

quadratic optimization in infinite-dimensional spaces |

quasiconvex relaxation |

quasilinear elliptic problems |

quotients of $C(K)$ spaces |

R |

Radon diffuse measure |

Radon measure |

random |

random differential complementarity system |

random differential inclusion |

random differential inclusions |

random fixed point |

Random fuzzy differential equations |

random fuzzy initial value problem |

random guiding function |

random periodic solution |

random topological degree |

rate of strong approximation |

reachable set in the space of measures |

reflexive Banach space |

reflexive Orlicz and Orlicz-Sobolev spaces |

regularity |

regularity condition |

relaxation |

relaxation theorem |

relaxations |

relaxed control |

relaxed controls |

renormalized solution |

residual selection |

resolvent operator |

resolvent operators |

retarded argument |

Riccati-Volterra equations |

Riemannian manifolds |

Riemann-Liouville and Hadamard integrals of fractional order |

robust function |

robust set |

robust set-valued map |

S |

saddle point |

saddle point theorem |

saddle-point conditions |

Saks spaces |

scalarly upper semi-continuous |

Schaefer's fixed point Theorem |

Schauder-Tychonoff fixed point |

Schr\"odinger equation |

second order nonlinear neutral delay differential equations |

second-order |

second-order derivatives |

second-order optimality conditions |

selection |

selections |

semi-continuous set-valued operators |

semicycle |

semigroup |

semigroup theory |

semi-inner product spaces |

semilinear differential inclusion |

semilinear differential inclusions |

semilinear equations |

sensitivities |

sensitivity analysis |

set valued integrals |

set-valued function |

set-valued functions |

set-valued integrals |

set-valued map |

set-valued mapping |

set-valued mappings |

set-valued random field |

set-valued semimartingals |

set-valued stochastic differential equation |

set-valued stochastic integral |

set-valued stochastic process |

set-valued stochastic processes |

shape optimization |

signal reconstruction |

sine series |

singular arcs |

singular perturbations |

Skorokhod |

smart controls |

Sobolev space |

solution |

solution depending on an arbitrary function |

solution set |

solutions set |

solvability |

spaces of vector-valued continuous functions |

spectral radius |

SQP methods |

stability |

state-dependent delay |

stationary feedback control |

Stepanov weighted ergodic components in general metric |

stochastic |

stochastic differential equations |

Stochastic differential inclusion |

stochastic differential inclusions |

stochastic differentials |

stochastic evolution equations on Banach spaces |

stochastic inclusions |

stochastic inclusions in the plane |

stochastic integro-differential equations |

stochastic integrodifferential equations |

stochastic processes |

stochastic systems |

strict topologies |

strictly differentiable function |

strong duality |

strong relaxation theorem |

strong solution |

strongly bounded operators |

structural acoustic model with thermal effects |

subcritical nonlinearities |

subdifferential evolution inclusion |

subdifferential operator |

subdifferentials |

subgradient method |

sufficient optimality condition |

summability of Fourier series |

superconductivity |

surjective map |

surjective operator |

sweeping process |

system of singular boundary value problems |

T |

tangency condition |

tangent cone |

tangential condition |

tangential conditions |

t-convex functions |

the Dirichlet boundary value problem |

thin films |

time-optimal problems |

topological degree |

topological dimension |

topological essentiality |

topology of simple convergence |

truncation function |

two - parameter stochastic process |

two-point bounadry value problem |

U |

unbounded perturbation |

uncertain systems |

uniform convergence |

Uniform space |

uniformly $\rho$-prox regular sets |

uniformly $\rho$-prox-regular sets |

unitary group |

upper semicontinuous |

upper solution |

upward functions |

usc and lsc multifunction |

usual strategies |

V |

vaccination |

variable exponent |

variable exponent $p(u)$-laplacian |

variable exponent Sobolev space |

variational inequalities |

variational inequality |

variational methods |

variational-type inequalities |

vector measure |

vector measures |

vector optimization |

vector valued measures |

velocity hodograph |

viability |

viable solution |

viable solutions |

vibration |

Vietoris map |

W |

wave equations |

weak compactness |

weak continuity |

weak sharp minimizer of order one |

weak solution |

weak solutions |

weakly precompact operators |

wedged |

weighted $p$-Laplacian |

weighted pseudo-ergodic components in general metric |

weighted Sobolev space |

Weyl weighted ergodic components in general metric |

X |

$X$-quasiconcave sets |

Y |

Yosida approximation |

Young measure |

Z |

zigzagging |