Interest in the mathematical analysis of multi-functions has increased rapidly over the past thirty years, partly because of its applications in fields such as biology, control theory and optimization, economics, game theory, and physics. Set Valued Mappings with Applications to Nonlinear Analysis contains 29 research articles from leading mathematicians in this area. The contributors were invited to submit papers on topics such as integral inclusion, ordinary and partial differential inclusions, fixed point theorems, boundary value problems, and optimal control. This collection will be of interest to researchers in analysis and will pave the way for the creation of new mathematics in the future.
Table of Contents
Positive L^TP and Continuous Solutions for Fredholm Integral Inclusions. A Note on the Structure of the Solution Set for the Cauchy Differential Inclusion in Banach Spaces. Fixed Point Theory for Acylic Maps between Topological Vector Spaces having Sufficiently many Linear Functionals, and Generalized Contractive Maps with Closed Values between Complete Metric Spaces. Using the Integral Manifolds to Solvability of Boundary Value Problems. On the Semicontinuity of Nonlinear Spectra. Existence Results for Two-Point Boundary Value Problems. Generalized Strongly Nonlinear Implicit Quasi-Variational Inequalities for Fuzzy Mappings. Vector Variational Inequalities, Multi-Objective Optimizations, Pareto Optimality and Applications. Variational Principle and Fixed Points. On the Baire Category Method in Existence Problems for Ordinary and Partial Differential Inclusions. Maximal Element Principles on Generalized Convex Spaces and their Applications. Fixed Point Results for Multi-valued Contractions on Gauge Spaces. The Study of Variational Inequalities and Applications to Generalized Complementarity Problems, Fixed Point Theorems of Set-Valued Mappings and Minimization Problems. Remarks on the Existence of Maximal Elements with Respect to a Binary Relation in Non-Compact Topological Spaces. Periodic Solutions of a Singularly Perturbed System of Differential Inclusions in Banach Space. Constrained Differential Inclusions. Nonlinear Boundary Value Problems with Multi-valued Terms. Optimal Control of a Class of Nonlinear Parabolic Problems with Multi-valued Terms. Continuation Theory for A-Proper Mappings and their Uniform Limits and Nonlinear Perturbations of Fredholm Mappings. Existence Theorems for Strongly Accretive Operators in Banch Spaces. A Kneser Type Property for the Solution Set of a Semilinear Differential Inclusion with Lower Semicontinuous Nonlinearity. A Nonlinear Multi-valued Problem with Nonlinear Boundary Conditions. Extensions of Monotone Sets. Convergence o
O'Regan, Donal; Agarwal, Ravi P.