Abstract Differential Equations And Nonlinear Mixed Problems

Abstract differential equations and nonlinear mixed problems

The present article is based on the Fermi Lectures I gave in May, 1985, at Scuola Normale Superiore, Pisa, in which I discussed various methods for solving the Cauchy problem for abstract nonlinear differential equations of evolution type. Here I present a detailed exposition of one of these methods, which deals with “elliptic-hyperbolic” equations in the abstract form and which has applications, among other things, to mixed initial-boundary value problems for certain nonlinear partial differential equations, such as elastodynamic and Schrödinger equations.

Abstract Differential Equations and Nonlinear Mixed Problems

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 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.