Multiplicity of solutions for a superlinear pp-Laplacian equation

We consider quasi-linear elliptic equations involving the pp-Laplacian with nonlinearities which interfere asymptotically with the spectrum of the differential operator. We show that such equations have for certain forcing terms at least two solutions. Such equations are of the so-called Ambrosetti–Prodi type. In particular, our theorem is a partial generalization of corresponding results for the semi-linear case by Ruf and Srikanth (1986) [2] and de Figueiredo (1988) [9].