Multiple solutions for image-Laplacian type equations Original Research Article

In this paper we establish the existence of three weak solutions of an equation which involves a general elliptic operator in divergence form (in particular, a pp-Laplacian operator), while the nonlinearity has a (p−1)(p−1)-sublinear growth at infinity. This result completes some recent papers, where mountain pass type solutions were obtained providing the nonlinear term via a (p−1)(p−1)-superlinear growth at infinity (fulfilling an Ambrosetti–Rabinowitz type condition). In our case, an abstract critical point result is applied, proved by G. Bonanno [G. Bonanno, Some remarks on a three critical points theorem, Nonlinear Analysis 54 (2003) 651–665].