Nonlinear Analysis and Boundary Value Problems: NABVP 2018, Santiago de Compostela, Spain, September 4-7 (Springer Proceedings in Mathematics & Statistics)

Description

This book is devoted to Prof. Juan J. Nieto, on the occasion of his 60th birthday. Juan José Nieto Roig (born 1958, A Coruña) is a Spanish mathematician, who has been a Professor of Mathematical Analysis at the University of Santiago de Compostela since 1991. His most influential contributions to date are in the area of differential equations. Nieto received his degree in Mathematics from the University of Santiago de Compostela in 1980. He was then awarded a Fulbright scholarship and moved to the University of Texas at Arlington where he worked with Professor V. Lakshmikantham. He received his Ph.D. in Mathematics from the University of Santiago de Compostela in 1983. Nieto's work may be considered to fall within the ambit of differential equations, and his research interests include fractional calculus, fuzzy equations and epidemiological models. He is one of the world’s most cited mathematicians according to Web of Knowledge, and appears in the Thompson Reuters Highly Cited Researchers list. Nieto has also occupied different positions at the University of Santiago de Compostela, such as Dean of Mathematics and Director of the Mathematical Institute. He has also served as an editor for various mathematical journals, and was the editor-in-chief of the journal Nonlinear Analysis: Real World Applications from 2009 to 2012. In 2016, Nieto was admitted as a Fellow of the Royal Galician Academy of Sciences. This book consists of contributions presented at the International Conference on Nonlinear Analysis and Boundary Value Problems, held in Santiago de Compostela, Spain, 4th-7th September 2018. Covering a variety of topics linked to Nieto’s scientific work, ranging from differential, difference and fractional equations to epidemiological models and dynamical systems and their applications, it is primarily intended for researchers involved in nonlinear analysis and boundary value problems in a broad sense. Preface Contents About the Editors A Variational Analogue of Krasnoselskii's Cone Fixed Point Theory 1 Introduction 2 Variational Analogue of the Compression Krasnoselskii's Cone Fixed Point Theorem 3 Variational Analogue of the Expansion Krasnoselskii's Cone Fixed Point Theorem 4 A General Scheme of Application to Semilinear Equations References Differentiability Properties of Solutions of a Second-Order Evolution Inclusion 1 Introduction 2 Preliminaries 3 The Main Results References How to Analytically Prove the Existence of Strange Attractors Using Measure Theory 1 Introduction 2 The Family mathbbF of Expanding Baker Maps 3 Preliminary Results 4 A Sketch of the Proof of Theorem 1.2 5 Proof of Corollary 1.3 References Initial Problems for Semilinear Degenerate Evolution Equations of Fractional Order in the Sectorial Case 1 Introduction 2 Nondegenerate Equation 2.1 Linear Equation 2.2 Semilinear Equation 3 Degenerate Equations 3.1 Resolving Operators Families 3.2 Degenerate Inhomogeneous Linear Equation 3.3 Degenerate Semilinear Equations 4 Application to a Class of Initial-Boundary Value Problems References Solvability for nth Order Coupled Systems with Full Nonlinearities 1 Introduction 2 Definitions and Preliminaries 3 Main Result 4 Lorentz-Lagrangian System Model 5 Coupled System of Two Korteweg-De Vries (KdV) Equations References Semilinear Equations in Banach Spaces with Lower Fractional Derivatives 1 Introduction 2 Equations Solved with Respect to the Highest Derivative 2.1 Linear Equation 2.2 Semilinear Equation 2.3 Application 3 Degenerate Equations 3.1 Example References Integral Boundary Value Problem for Intuitionistic Fuzzy Partial Hyperbolic Differential Equations 1 Introduction 2 Preliminaries 3 Existence and Uniqueness 4 Solving Intuitionistic Fuzzy PHDEs with Integral Boundary Conditions 5 Application 6 Conclusion References On the Periodic Ricker Equation 1 Introduction 2 Some Useful Tools in One-Dimensional Dynamics 3 Periodic Ricker Family References The Stability of Vortices in Gas on the l-Plane: The Influence of Centrifugal Force 1 Reduction of 3D Primitive Equations of the Atmosphere Dynamics to the l-Plane Model 2 Motion with Uniform Deformation: Steady States and Their Stability 2.1 δ = 0 2.2 δ=1, s=1 2.3 δ=1, s=sinθ 3 Study of System (7), (8) in the Lagrangian Coordinates 3.1 First Integrals 3.2 Representation of Solution 4 Discussion References Results for Fractional Differential Equations with Integral Boundary Conditions Involving the Hadamard Derivative 1 Introduction 2 Preliminaries 3 An Existence, Uniqueness and Location Result 4 Example References A Nonlinear Problem Related to Artificial Circulation in a Lake 1 The Environmental Problem 2 Mathematical Formulation of the Problem 3 Mathematical Analysis of the Problem References The Fučík Spectrum as Two Regular Curves 1 Introduction 2 Preliminaries 3 Implicit Description of the Fučík Spectrum for α,β> 0 4 The Fučík Spectrum as Parametrized Curves References Duffing Equation with Nonlinearities Between Eigenvalues 1 Introduction 2 Preliminaries 3 Existence Theorem References Comparison and Uniqueness Results for the Periodic Boundary Value Problem for Linear First-Order Differential Equations Subject to a Functional Perturbation 1 Introduction 2 General Comparison Result 3 Particular Cases 3.1 Retarded Functional Differential Equations 3.2 Minimum Case 3.3 Integral Case 4 Generalization of Theorem 1 5 Nonnegativity of Solutions 5.1 Retarded Functional Differential Equations 5.2 Maximum Case 5.3 Integral Case 6 Uniqueness of Solution References Time-Fractional Optimal Control of Initial Value Problems on Time Scales 1 Introduction 2 Preliminaries 2.1 Time-Scale Essentials 2.2 Fractional Derivative and Integral on Time Scales 2.3 Properties of the Time-Scale Fractional Operators 2.4 Existence of Solutions to Fractional IVPs on Time Scales 3 Main Results 3.1 Fractional Integration by Parts on Time Scales 3.2 Nonlinear Riemann–Liouville FOCPs on Time Scales 3.3 An Illustrative Example 4 Conclusion References Relationship Between Green's Functions for Even Order Linear Boundary Value Problems 1 Introduction 2 Preliminary Results 3 Decomposing Green's Functions 3.1 Neumann Problem 3.2 Dirichlet Problem 3.3 Mixed Problems 3.4 Connecting Relations Between Different Problems 4 Decomposition of the Spectra 5 Constant Sign of Green's Functions 6 Comparison Principles References Random Evolution Equations with Bounded Fractional Integral-Feedback 1 Introduction 2 Abstract Setting and Augmented Model 3 Well-Posedness 4 Random Stabilization 5 Applications 5.1 Heat Equation with Fractional Integral Damping 5.2 Integral Fractional Damped Random Wave Equation References