Multiple solutions of nonlinear partial functional differential equations and systems

摘要

We shall consider weak solutions of initial-boundary value problems for semilinear and nonlinear parabolic differential equations with certain nonlocal terms, further, systems of elliptic functional differential equations. We shall prove theorems on the number of solutions and find multiple solutions. These statements are based on arguments for fixed points of some real functions and operators, respectively, and existence-uniqueness theorems on partial differential equations (without functional terms).