Nonlinear analysis, differential equations, and applications / Themistocles M. Rassias, editor.

Format:

Book

Contributor:

Rassias, Themistocles M., editor.

Series:

Springer optimization and its applications ; Volume 173.

Springer optimization and its applications ; Volume 173

Language:

English

Subjects (All):

Functional equations.

Physical Description:

1 online resource (791 pages)

Place of Publication:

Cham, Switzerland : Springer, [2021]

Summary:

This contributed volume showcases research and survey papers devoted to a broad range of topics on functional equations, ordinary differential equations, partial differential equations, stochastic differential equations, optimization theory, network games, generalized Nash equilibria, critical point theory, calculus of variations, nonlinear functional analysis, convex analysis, variational inequalities, topology, global differential geometry, curvature flows, perturbation theory, numerical analysis, mathematical finance and a variety of applications in interdisciplinary topics. Chapters in this volume investigate compound superquadratic functions, the Hyers-Ulam Stability of functional equations, edge degenerate pseudo-hyperbolic equations, Kirchhoff wave equation, BMO norms of operators on differential forms, equilibrium points of the perturbed R3BP, complex zeros of solutions to second order differential equations, a higher-order Ginzburg-Landau-type equation, multi-symplectic numerical schemes for differential equations, the Erdős-Rényi network model, strongly m -convex functions, higher order strongly generalized convex functions, factorization and solution of second order differential equations, generalized topologically open sets in relator spaces, graphical mean curvature flow, critical point theory in infinite dimensional spaces using the Leray-Schauder index, non-radial solutions of a supercritical equation in expanding domains, the semi-discrete method for the approximation of the solution of stochastic differential equations, homotopic metric-interval L-contractions in gauge spaces, Rhoades contractions theory, network centrality measures, the Radon transform in three space dimensions via plane integration and applications in positron emission tomography boundary perturbations on medical monitoring and imaging techniques, the KdV-B equation and biomedical applications.

Contents:

Intro

Preface

Contents

On Compound Superquadratic Functions

1 Introduction

2 Refinements of Jensen's Inequality via Compound Functions

3 The Quasi-Mean Ff( x,λ)

References

Best Hyers-Ulam Stability Constants on a Time Scale with Discrete Core and Continuous Periphery

2 Time Scale with Discrete Core and Continuous Periphery

3 Best Constants for First-Order Equations with Constant Complex Coefficient

4 Connection with h-Difference Equations in the Case |1+hλ|&gt

1

5 Conclusion and Future Directions

Invariance Solutions and Blow-Up Property for Edge Degenerate Pseudo-Hyperbolic Equations in Edge Sobolev Spaces

2 Edge Sobolev Spaces

3 Some Auxiliary Results

4 Invariance of the Solutions

5 Global Existence and Finite-Time of the Solutions

ϕ4 Solitons in Kirchhoff Wave Equation

2 SSB in ϕ4 Scalar Field Theory: The Kink Solitons

3 Kirchhoff Wave Function, Energy and Potential

4 The Kpd Produced from Classical Field Theory

5 SSB in the Kpd

6 Conclusions

Appendix: Estimation of the Potential Density U(ϕ)

Estimates for Lipschitz and BMO Norms of Operators on Differential Forms

2 Local Poincaré-Type Inequalities

3 Estimates for BMOs and locLipαs Norms

4 Applications

Application of Boundary Perturbations on Medical Monitoring and Imaging Techniques

1.1 Boundary Perturbations. A Short Introduction

2 Mathematical Formulation of Medical Monitoring Techniques. Electroencephalography and Magnetoencephalography

2.1 The Influence of Geometric Variations on the Forward Problem

2.1.1 EEG

2.1.2 MEG

2.2 The Influence of Geometric Variations on the Inversion Algorithm

2.2.1 EEG

2.2.2 MEG

3 Example

3.1 EEG.

3.2 MEG

4 Conclusions and Discussion

Poynting-Robertson and Oblateness Effects on the Equilibrium Points of the Perturbed R3BP: Application on Cen X-4 Binary System

2 Equations of Motion

3 Existence and Positions of Equilibrium Points

4 Stability of the Non-collinear Equilibrium Points

5 Numerical Application

6 Discussion and Conclusion

Localization and Perturbation of Complex Zeros of Solutions to Second Order Differential Equations with Polynomial Coefficients. A Survey

2 Solution Estimates for ODEs

3 Singular Values of Compact Operators

4 Bounds for Zeros of Entire Functions via Taylor Coefficients

5 Bounds for Sums and Products of Zeros of an Entire Function via Its Order

6 Sums and Products of Zeros of Solutions to Homogeneous ODEs with Polynomial Coefficients

7 Applications of Theorem 3

8 A Perturbation Bound for the Zeros of Entire Functions in Terms of Taylor Coefficients

9 Proof of Theorem 4

10 A Perturbation Bound for the Zeros of an Entire Function via Its Order

11 An Estimate for the Difference of Two Solutions

12 Perturbations of the Zeros of Solutions to ODEs

13 Example to Theorem 6

Dynamics of a Higher-Order Ginzburg-Landau-Type Equation

2 Limit Set and Collapse

2.1 Existence of the Limit Set

2.2 Conditions for Collapse

3 Soliton Dynamics: Perturbative Approach

3.1 Perturbation Theory for Bright Solitons (s=-1)

3.2 Perturbation Theory for Dark Solitons (s=+1)

3.3 Solitons and Shock Waves in an Effective KdV-Burgers Picture

The Role of Differential Equations in Applied Statistics

2 Theoretical Framework for the Nonlinear Design

3 Growth Curves

4 Differential Equations in Probability

4.1 Brownian Motion.

4.2 Pure Birth Process

4.3 The Birth-and-Death Process

5 Discussion

Appendix 1

Appendix 2: Introduction to Heat Equation

Geometric Derivation and Analysis of Multi-Symplectic Numerical Schemes for Differential Equations

1 Introduction and Motivation

2 Review of Variational Integrators

3 Exponential Integrators

3.1 Exponential High Order Variational Integrators

3.2 Frequency Estimation for Mass Points Motion in Three Dimensions

4 Triangle and Square Discretization

4.1 Triangle Discretization

4.2 Square Discretization

5 Numerical Examples Using Triangle Discretization

5.1 Linear Wave Equation

5.2 Laplace Equation

5.3 Poisson Equation

6 Numerical Examples Using Square Discretization

6.1 Klein-Gordon

7 Analysis of the Proposed Schemes

7.1 Dispersion Analysis

7.2 Convergence Experiments

8 Summary and Conclusions

Appendix

Non-radial Solutions of a Supercritical Equation in Expanding Domains: The Limit Case

2 Notations and Some Background Material

3 Preliminary Results

4 Solution of the Problem (P)

Financial Contagion in Interbank Networks: The Case of Erdős -Rényi Network Model

2 Related Literature

3 Erdős-Rényi Random Graph Model

3.1 The Mathematical Description of the Contagion Model

3.2 The Interbank Network

3.3 Shock Propagation and Contagion Dynamics

3.4 Monte Carlo simulations

4 Main Findings

4.1 Computer Experiments

4.2 Simulation Results

5 Conclusions

Higher Order Strongly m-convex Functions

2 m-Convex Functions

3 Strongly m-Convex Functions

4 Properties of Strongly m-Convex Functions

5 Applications

Conclusion

Characterizations of Higher Order Strongly Generalized Convex Functions.

1 Introduction

2 Formulations and Basic Facts

3 Generalized Convex Functions

4 Higher Order Strongly Generalized Convex Functions

5.1 Generalized Variational Inequalities

A Note on Generalized Nash Games Played on Networks

2 Network Games

2.1 Elements of Graph Theory and Game Classes

2.2 The Linear-Quadratic Model

3 Generalized Nash Equilibrium Problems on Networks

3.1 An Overview of GNEPs and the Variational Inequality Approach to their Solution

3.2 A Linear-Quadratic Network GNEP

4 Numerical Experiments

5 Conclusions and Further Research Perspectives

Piecewise Polynomial Inversion of the Radon Transform in Three Space Dimensions via Plane Integration and Applications in Positron Emission Tomography

2 The Radon Transform in Two Space Dimensions

3 The Radon Transform in Three Space Dimensions

4 The Inversion of the Radon Transform in Three Space Dimensions via Plane Integration

5 Numerical Implementation of the Inversion of the Radon Transform in Three Space Dimensions via Piecewise Cubic Polynomials

Factorization and Solution of Linear and Nonlinear Second Order Differential Equations with Variable Coefficients and Mixed Conditions

2 Preliminaries

3 Factorization Method for Linear Differential Equations

4 Factorization Method for Nonlinear Differential Equations

A General Framework for Studying Certain Generalized Topologically Open Sets in Relator Spaces

1 Motivations

3 A Few Basic Facts on Relations

4 A Few Basic Facts on Relators

5 Structures Derived from Relators

6 Further Structures Derived from Relators

7 Closure Operations for Relators.

8 Some Further Theorems on the Operations and

9 Projection Operations for Relators

10 Reflexive, Non-partial and Non-degenerated Relators

11 Topological and Quasi-Topological Relators

12 Proximal and Quasi-Proximal Relators

13 A Few Basic Facts on Filtred Relators

14 A Few Basic Facts on Quasi-Filtered Relators

15 Some Further Theorems on Topologically Filtered Relators

16 Some More Particular Theorems on Topologically Filtered Relators

17 Some Generalized Topologically Open Sets

18 Some Further Theorems on Generalized Topologically Open Sets

19 A Further Family of Generalized Topologically Open Sets

20 Some Further Theorems on the Family AR

21 Characterizations of the Family AR

22 Some Further Characterizations of the Family AR

23 Lower and Upper Nearness Relations for Sets

24 Some Set-Theoretic Properties of the Relation `3́9`42`"̇613A``45`47`"603ALnR

25 Some Topological Properties of the Relation `3́9`42`"̇613A``45`47`"603ALnR

26 Some Further Topological Properties of the Relation `3́9`42`"̇613A``45`47`"603ALnR

27 Some Relation-Theoretic Properties of the Relation `3́9`42`"̇613A``45`47`"603ALnR

28 Lower and Upper Nearness Closures of Families of Sets

29 Some Set-Theoretic Properties of the Families A and Au

30 Intersection Properties of the Families A and Au

31 Some Algebraic and Topological Properties of the Operations and u

32 Nearness Closures of the Families TR, TRs and TRp

33 Some Further Theorems on the Families TRs and TRp

34 Some Basic Properties of the Families TRsu and TRp

35 Some Further Theorems on the Closure Operation

36 An Illustrating Diagram and Two Related Examples

Graphical Mean Curvature Flow

2 Riemannian Submanifolds

2.1 Notation and Conventions

2.2 The Pull-back Bundle.

2.3 The Second Fundamental Form.

Notes:

Description based on print version record.

ISBN:

3-030-72563-4