Multiple Solutions for a Class of Bi-nonlocal Problems with Nonlinear Neumann Boundary Conditions

In this paper, we are interested in a class of bi-nonlocal problems with nonlinear Neumann boundary conditions and sublinear terms at infinity. Using (S+) mapping theory and variational methods, we establish the existence of at least two non-trivial weak solutions for the problem provided that the parameters are large enough. Our result complements and improves some previous ones for the superlinear case when the Ambrosetti-Rabinowitz type conditions are imposed on the nonlinearities.