Multiplicity of solutions for homogeneous elliptic systems with critical growth

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Furtado, Marcelo F.²  da Silva, Joao Pablo P.¹ 

[1] Fed Univ Para, Dept Matemat, BR-66075110 Belem, Para, Brazil

[2] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

关键词: Elliptic systems;    Critical problems;    Category of Ljusternik-Schnirelmann;    Homogeneous problems;   

DOI  :  10.1016/j.jmaa.2011.07.001

来源: Elsevier

【 摘 要 】

In this paper we are concerned with the number of nonnegative solutions of the elliptic system {-Delta u = Q(u)(u, v) + 1/2*H(u)(u, v), in Omega, -Delta v = Q(v)(u, v) + 1/2*H(v)(u, v), in Omega, u = v = 0, on partial derivative Omega, where Omega subset of R(N) is a bounded smooth domain, N >= 4, 2* := 2N/(N - 2) and Q(u), H(u) and Q(v), H(v) are the partial derivatives of the homogeneous functions Q, H is an element of C(1) (R(+)(2), R), where R(+)(2) := [0, infinity) x [0, infinity). In the proofs we apply variational methods and Ljusternik-Schnirelmann theory. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free