On the solvability of nonlinear noncompact operator equations

The notion of (p, k)-epi mappings is introduced. The properties of such mappings are studied and the results obtained are applied to some differential equations. 1980 Mathematics subject classification (Amer. Math. Soc): primary 47 H 15; secondary 47 H 10, 34 K 10, 35 L 15

Topological methods for set-valued nonlinear analysis

This book provides a comprehensive overview of the authors’ pioneering contributions to nonlinear set-valued analysis by topological methods. The coverage includes fixed point theory, degree theory, the KKM principle, variational inequality theory, the Nash equilibrium point in mathematical economics, the Pareto optimum in optimization, and applications to best approximation theory, partial equations and boundary value problems. Self-contained and unified in presentation, the book considers the existence of equilibrium points of abstract economics in topological vector spaces from the viewpoint of Ky Fan minimax inequalities. It also provides the latest developments in KKM theory and degree theory for nonlinear set-valued mappings