Existence of solutions to various classes of nonlinear elliptic differential equations and their applications

Abstract

This thesis is devoted to the study of various classes of nonlinear elliptic partial differential equations with nonlocal terms, which arise from many disciplinary fields. By using the variational method, the topological method and the scaling technique, we establish the existence and nonexistence of solutions, multiple solutions and symmetric properties of solutions for these nonlinear partial differential equations.