Multiple positive solutions for p-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term
Multiple positive solutions for p-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term
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涉及凹凸非线性和 Hardy 型项的 p-拉普拉斯椭圆方程的多个正解
DOI：
10.1016/j.na.2010.09.017
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发表时间：
2011-01-15
影响因子：
1.4
通讯作者：
Kang, Dongsheng
中科院分区：
文献类型：
--
作者：
Wang, Li;Wei, Qiaoling;Kang, Dongsheng
本文考虑以下问题：{-Delta(p)u - mu 竖条 u 竖条(p-2)u 竖条 x 竖条(p) = lambda f (x)竖条 u 竖条(q-2)u + g(x)竖条 u 竖条(p)*(-2)u，x 是 Omega 的元素，u = 0，x 是 Omega 的元素，其中 R(N) 的 Omega 子集是有界域，例如0 是 Omega 的元素，1 < q < p，lambda > 0，mu < 、f 和 g 是非负函数，(mu) over bar = (N-p/p)(p) 是最佳 Hardy 常数，p* = Np/N-p 是临界 Sobolev 指数。通过提取Nehari流形中的Palais-Smale序列，验证了该方程存在多个正解。 (C) 2010 Elsevier Ltd. 保留所有权利。
In this paper, the following problem is considered:{-Delta(p)u - mu vertical bar u vertical bar(p-2)u vertical bar x vertical bar(p) = lambda f (x)vertical bar u vertical bar(q-2)u + g(x)vertical bar u vertical bar(p)*(-2)u, x is an element of Omega, u = 0, x is an element of Omega,where Omega subset of R(N) is a bounded domain such that 0 is an element of Omega, 1 < q < p, lambda > 0, mu < , f and g are nonnegative functions, (mu) over bar = (N-p/p)(p) is the best Hardy constant and p* = Np/N-p is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple positive solutions to this equation is verified. (C) 2010 Elsevier Ltd. All rights reserved.