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This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and app...

This book presents the foundation of the theory of almost automorphic functions in abstract spaces and the theory of almost periodic functions in locally and non-locally convex spaces and their applications in differential equations. Since the publication of Almost automorphic and almost periodic functions in abstract spaces (Kluwer Academic/Plenum, 2001), there has been a surge of interest in the theory of almost automorphic functions and app...

This monograph is aimed at presenting smooth and unified generalized fractional programming (or a program with a finite number of constraints). Under the current interdisciplinary computer-oriented research environment, these programs are among the most rapidly expanding research areas in terms of its multi-facet applications and empowerment for real world problems that can be handled by transforming them into generalized fractional programmin...

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Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of invariant s- spaces, uniform spectrum), and new concepts (almost periodicity and almost automorphy in fuzzy settings) have been introduced in the literature. The range of applications incl...

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new...

Since the publication of our first book [80], there has been a real resiu-gence of interest in the study of almost automorphic functions and their applications ([16, 17, 28, 29, 30, 31, 32, 40, 41, 42, 46, 51, 58, 74, 75, 77, 78, 79]). New methods (method of invariant s- spaces, uniform spectrum), and new concepts (almost periodicity and almost automorphy in fuzzy settings) have been introduced in the literature. The range of applications incl...

This book presents and discusses new developments in the study of evolution equations. Topics discussed include a qualitative study of a perturbed critical semi-linear wave equation in variable metric, renormalised solution for a non-linear anisotropic degenerate parabolic equation, periodic solutions of impulsive evolution equations, non-linear spectral theory and controllability of semi-linear evolution equations, uniform exponential stabili...

This book presents high-quality research from around the world on the theory and methods of linear or nonlinear evolution equations as well as their further applications. Equations dealing with the asymptotic behavior of solutions to evolution equations are included. The book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic...

CONTENTS: Preface, A Bit of Quantum Mechanics, Operators in Hilbert Spaces, Spectral Theorem for Self-adjoint Operators, Compact Operators and the Hilbert-Schmidt Theorem, Elements of Perturbation Theory, Variational Principles, One-Dimensional Schrödinger Operator, Multidimensional Schrödinger Operator, Periodic Schrödinger Operator, Quantum Graphs, Non-linear Schrödinger Equation, References, Index.

This book presents high-quality research on the theory and methods of linear or non-linear evolution equations as well as their further applications. Equations dealing with the asymptotic behaviour of solutions to evolution equations are included. This book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and quasi-periodic solutions, concave...

This book contains high-quality papers on the theory and methods of linear or non-linear evolutions as well as their further applications.

Handbook of Evolution Equations

This book presents and discusses new developments in the study of differential equations. Topics discussed include pseudo almost automorphic solutions for some non-linear differential equations, positive solutions for p-laplacian dynamic delay differential equations on time scales, semi-linear fractional differential equations, positive solutions for a class of second-order impulsive singular differential equations in banach spaces and non-lin...

This book presents and discusses new developments in the study of evolution equations. Topics discussed include global attractors for semi-linear parabolic equations with delays, exact controllability for the vibrating plate equation in a non smooth domain, weighted pseudo almost automorphic solutions for some partial functional differential equations in fading memory spaces, periodic solutions to the non-linear parabolic equation, and infinit...

This book presents and discusses new developments in the study of evolution equations. Topics discussed include parabolic equations, generalised gradient in weak maximum principle with non-differentiable drift, bifluid systems, Yamabe-type flows, stochastic evolution equations, heat equations, Navier-Stokes equations, Cahn-Hilliard equations, and more.

Almost Automorphic and Almost Periodic Functions in Abstract Spaces introduces and develops the theory of almost automorphic vector-valued functions in Bochner's sense and the study of almost periodic functions in a locally convex space in a homogenous and unified manner. It also applies the results obtained to study almost automorphic solutions of abstract differential equations, expanding the core topics with a plethora of groundbreaking new...

Presents the research on the theory and methods of linear and non-linear evolution equations as well as their further applications. This book includes the asymptotic behavior of solutions to evolution equations. It also covers other non-linear differential equations and applications to natural sciences.

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This book presents, recent and important research from around the world on the theory and methods of linear or non-linear evolution equations as well as their further applications. Equations dealing with the asymptotic behaviour of solutions to evolution equations are included. This book also covers degenerate parabolic equations, abstract differential equations, comments on the Schrodinger equation, solutions in banach spaces, periodic and qu...