Positive solutions and eigenvalue intervals for a second order p-Laplacian discrete system

Abstract

In this paper, we investigate the existence of at least one positive solution to a second order p-Laplacian discrete system. As applications, we characterize the eigenvalue intervals for one typical n-dimensional system. The proof is based on a well-known fixed point theorem in cones.

Weak solutions to Neumann discrete nonlinear system of Kirchhoff type

“…This method was successfully used by Bonanno et al [1] for the study of an eigenvalue nonhomogeneous Neumann problem, where, under an appropriate oscillating behaviour of the nonlinear term, they proved the existence of a determined open interval of positive parameters for which the problem considered admits infinitely many weak solutions that strongly converge to zero, in an appropriate Orlicz Sobolev space. Motivated by the work of [13] where J. Zhao proved the existence of positive solutions, the approach presented in this article is different than the one given in the papers mentioned above. To the best of our knowledge , results on existence of weak solutions of system (1.1), using minimization method, have not been found in the literature.…”