In this paper we study the existence of at least two nontrivial solutions for the nonlinear p-Laplacian problem, with nonlinear boundary conditions. We establish that there exist at least two solutions, which are opposite signs. For this reason, we characterize the first eigenvalue of an intermediary eigenvalue problem by the minimization method. In fact, in some sense, we establish the non-resonance below the first eigenvalues of nonlinear Steklov-Robin problem.

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