Existence of multiple solutions for an elliptic system with sign-changing weight functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:395

Article

Xiu, Zonghu^1,2  Chen, Caisheng¹  Huang, Jincheng¹ 

[1] Hohai Univ, Coll Sci, Nanjing 210098, Jiangsu, Peoples R China

[2] Qingdao Agr Univ, Sci & Informat Coll, Qingdao 266109, Peoples R China

关键词: Nehari manifold;    Singular quasilinear elliptic system;    Concave and convex nonlinearities;   

DOI  :  10.1016/j.jmaa.2012.05.059

来源: Elsevier

【 摘 要 】

In this paper, we will consider a class of quasilinear elliptic problem of the form integral-diu (vertical bar x vertical bar-(ap)vertical bar del u vertical bar(p-2)vertical bar del u vertical bar + g(1)(x)vertical bar u vertical bar(p-2)u = alpha/alpha+beta h(x)vertical bar u vertical bar(alpha-2)u vertical bar v vertical bar(beta) + lambda H-1(x)vertical bar u vertical bar(n-2) u, -div(vertical bar x vertical bar(-ap)vertical bar del u vertical bar(p-2)del u) + g(2) (x) vertical bar v vertical bar(p-2) v =beta/alpha+beta h(x)vertical bar v vertical bar(beta-2) v vertical bar v vertical bar(alpha) + mu H-2 (x)vertical bar v vertical bar(n-2) v, u(x) > 0, v(x) > 0, x is an element of R-N, where lambda, mu > 0, 1 < p < N, 1 < n < p < alpha + beta < p* = Np/N-pd, 0 <= a < N-p/p a <= b < a + 1, d = a + 1 - b > 0, the weight g(1)(x), g(2)(x) are bounded and nonnegative functions and h(x), H-1 (x), H-2 (x) are continuous functions which change sign in R-N. We will prove that the problem has at least two positive solutions by using the Nehari manifold and the fibering maps associated with the Euler function for this problem. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

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