Existence and multiplicity of positive solutions for a class of semilinear elliptic system with nonlinear boundary conditions

Subject Areas : History and biography

F. M. Yaghoobi ¹ , J. Shamshiri ²

1 - Department of Mathemetics, College of Science, Hamedan Branch, Islamic Azad University, Hamedan, Iran
2 - Department of Mathematics, Mashhad Branch, Islamic Azad University, Mashhad, Iran

Received: 2015-12-29 Accepted : 2016-03-01 Published : 2016-06-01

Keywords: Critical point, Semilinear elliptic system, Nonlinear boundary value problem, Fibering map, Nehari manifold,

Abstract :

This study concerns the existence and multiplicity of positive weak solutions for a class ofsemilinear elliptic systems with nonlinear boundary conditions. Our results is depending onthe 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 withpositive energy.

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