Multiple solutions for a class of semilinear elliptic problems with Robin boundary condition

In this paper, we show the existence of at least four nontrivial solutions for a class of semilinear elliptic problems with Robin boundary condition and jumping nonlinearities. Solvability of oscillating equations with Robin boundary condition is also investigated. We prove the conclusions by using sub-super-solution method, Fučík spectrum theory, mountain pass theorem in order intervals and Morse theory.