Eigenproblem for p-Laplacian and nonlinear elliptic equation with nonlinear boundary conditions

In this article, we study the solvability of nonlinear problem for p-Laplacian with nonlinear boundary conditions. We give some characterization of the first eigenvalue of an intermediary eigenvalue problem as simplicity, isolation and its strict monotonicity. Afterward, we character also the second eigenvalue and its strictly partial monotony. On the other hand, in some sense, we establish the non-resonance below the first and furthermore between the first and second eigenvalues of nonlinear Steklov-Robin.