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Nonlinear Analysis, Differential Equations, and Applications

  • Book
  • © 2021

Overview

Editors:
  1. Themistocles M. Rassias

    1. Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

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  • Self-contained presentation of results
  • Particularly useful for graduate students and researchers conducting interdisciplinary research
  • The detailed results presented will appeal to a wide readership

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 173)

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Table of contents (26 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. On Compound Superquadratic Functions

    • Shoshana Abramovich
    Pages 1-15

  3. Best Hyers–Ulam Stability Constants on a Time Scale with Discrete Core and Continuous Periphery

    • Douglas R. Anderson, Masakazu Onitsuka
    Pages 17-37

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

    • Carlo Cattani, Morteza Koozehgar Kalleji
    Pages 39-70

  5. ϕ 4 Solitons in Kirchhoff Wave Equation

    • Y. Contoyiannis, P. Papadopoulos, M. Kampitakis, S. M. Potirakis, N. L. Matiadou
    Pages 71-80

  6. Estimates for Lipschitz and BMO Norms of Operators on Differential Forms

    • Shusen Ding, Guannan Shi, Yuming Xing
    Pages 81-99

  7. Application of Boundary Perturbations on Medical Monitoring and Imaging Techniques

    • M. Doschoris, A. Papargiri, V. S. Kalantonis, P. Vafeas
    Pages 101-130

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

    • Aguda Ekele Vincent, Angela E. Perdiou
    Pages 131-147

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

    • Michael Gil’
    Pages 149-186

  10. Dynamics of a Higher-Order Ginzburg–Landau-Type Equation

    • Theodoros P. Horikis, Nikos I. Karachalios, Dimitrios J. Frantzeskakis
    Pages 187-207

  11. The Role of Differential Equations in Applied Statistics

    • Christos P. Kitsos, C. S. A. Nisiotis
    Pages 209-230

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

    • Odysseas Kosmas, Dimitrios Papadopoulos, Dimitrios Vlachos
    Pages 231-251

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

    • Nikos Labropoulos
    Pages 253-276

  14. Financial Contagion in Interbank Networks: The Case of Erdős–Rényi Network Model

    • K. Loukaki, P. Boufounou, J. Leventides
    Pages 277-317

  15. Higher Order Strongly m-convex Functions

    • Muhammad Aslam Noor, Khalida Inayat Noor
    Pages 319-339

  16. Characterizations of Higher Order Strongly Generalized Convex Functions

    • Muhammad Aslam Noor, Khalida Inayat Noor, Michael Th. Rassias
    Pages 341-364

  17. A Note on Generalized Nash Games Played on Networks

    • Mauro Passacantando, Fabio Raciti
    Pages 365-380

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

    • Nicholas E. Protonotarios, George A. Kastis, Nikolaos Dikaios, Athanassios S. Fokas
    Pages 381-396

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

    • E. Providas
    Pages 397-414

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

    • Themistocles M. Rassias, Árpád Száz
    Pages 415-491
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Keywords

About this book

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.



Editors and Affiliations

  • Department of Mathematics, Zografou Campus, National Technical University of Athens, Athens, Greece

    Themistocles M. Rassias

About the editor

Themistocles M. Rassias is professor of mathematics at the National Technical University of Athens. His research interests include nonlinear analysis, global analysis, approximation theory, functional analysis, functional equations, inequalities and their applications. Professor Rassias received his PhD in mathematics from the University of California, Berkeley in 1976; his thesis advisor was Stephen Smale and his academic advisor was Shiing-Shen Chern. In addition to his extensive list of journal publications, Professor Rassias has published as author or volume editor several books published with Springer. Th. M. Rassias has received several awards and is an active editorial board member of an array of journals in mathematical analysis and optimization. His publications have received a large number of citations, with h-index 47.

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