Fucik spectrum, sign-changing and multiple solutions for semilinear elliptic boundary value problems with jumping nonlinearities at zero and infinity

In this paper, Fucik spectrum, ordinary differential equation theory of Banach spaces and Morse theory are used to study semilinear elliptic boundary value problems with jumping nonlinearities at zero or infinity, and some new results on the existence of nontrivial solutions, multiple solutions and sign-changing solutions are obtained. In one case seven nontrivial solutions are got. The techniques have independent interest.