1Department of Mathemetics, College of Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran
This study concerns the existence and multiplicity of positive weak solutions for a class of semilinear elliptic systems with nonlinear boundary conditions. Our results is depending on the local minimization method on the Nehari manifold and some variational techniques. Also by using Mountain Pass Lemma, we establish the existence of at least one solution with positive energy.