Multiple positive solutions for semilinear elliptic systems with nonlinear boundary condition

In this paper, we study the nonlinear boundary value problem ÀDu þ u ¼ fuðu; vÞ in X; ÀDv þ v ¼ fvðu; vÞ in X; ou on ¼ guðu; vÞ; ov on ¼ gvðu; vÞ on oX; 8 >< >: where X is a bounded domain in RN with smooth boundary and the pairs of ðfu; fvÞ and ðgu; gvÞ are subcritical nonlinearities. With the help of the Nehari manifold, we show existence of at least two positive solutions when one of the pairs of ðfu; fvÞ and ðgu; gvÞ is sublinear and the other one superlinear. Ó 2006 Elsevier Inc. All rights reserved.

• Type: Journal
• Year: 2007
• Where: AMC
• Authors: Tsung-fang Wu
• Keywords: AMC 2007, Nonlinear Boundary Value, Problem Àdu, Smooth Boundary