Nonlinear Analysis, Differential Equations, and Applications

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 HyersUlam 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 GinzburgLandau-type equation, multi-symplectic numerical schemes for differential equations, the Erds-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.

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

Auteur

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.

Texte du rabat

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 Erdos-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.

Contenu
On compound superquadratic functions (Abramovich).- Best HyersUlam stability constants on a time scale with discrete core and continuous periphery (Anderson).- Invariance solutions and blow-up property for edge degenerate pseudo-hyperbolic equations in edge Sobolev spaces (Cattani).- f4 solitons in Kirchhoff wave equation (Papadopoulos).- Estimates for Lipschitz and BMO norms of operators on differential forms (Ding).- Application of boundary perturbations on medical monitoring and imaging techniques (Kalantonis).- Poynting-Robertson and oblateness effects on the equilibrium points of the perturbed R3BP: Application on Cen X-4 binary system (Perdiou).- Localization and perturbation of complex zeros of solutions to second order differential equations with polynomial coefficients. A survey (Gil).- Dynamics of a higher-order GinzburgLandau-type equation (Horikis).- The role of differential equations in applied statistics (Kitsos).- Geometric derivation and analysis of multi-symplectic numerical schemes for differential equations (Vlachos).- Non-radial solutions of a supercritical equation in expanding domains: The limit case (Labropoulos).- Financial contagion in interbank networks: The case of Erds-Rényi network model (Leventides).- Higher order strongly m-convex functions (Noor).- Characterizations of higher order strongly generalized convex functions (Noor).- A note on generalized Nash games played on networks (Raciti).- Piecewise polynomial inversion of the Radon transform in three space dimensions via plane integration and applications in positron emission tomography (Protonotarios).- Factorization and solution of linear and nonlinear second order differential equations with variable coefficients and mixed conditions (Providas).- A General framework for studying certain generalized topologically open sets in relator spaces (Szaz).- Graphical mean curvature flow (Savas-Halilaj).- Critical point theory in infinite dimensional spaces using the Leray-Schauder index (Schechter).- Canonical systems of partial differential equations (Schechter).- The Semi-Discrete Method for the approximation of the solution of stochastic differential equations (Stamatiou).- Homotopic metric-interval L-contractions in gauge spaces (Turinici).- Analytic methods in Rhoades contractions theory (Turinici).- Nonlinear dynamics of the KdV-B equation and its biomedical applications (Xenos).