Sign-Changing and Multiple Solutions Theorems for Semilinear Elliptic Boundary Value Problems with Jumping Nonlinearities

In this paper, we use the ordinary differential equation theory of Banach spaces and minimax theory, and in particular, the relative mountain pass lemma to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity, and get new multiple solutions and sign-changing solutions theorems, at last we get up to six nontrivial solutions.