Multiple positive solutions for p-Laplace elliptic equations involving concave-convex nonlinearities and a Hardy-type term

作者：Wang, Li; Wei, Qiaoling; Kang, Dongsheng^*

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(2): 626-638.

DOI：10.1016/j.na.2010.09.017

• Solution
• Critical exponent
• Hardy inequality
• Concave-convex
• Variational method

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 < <(mu)over bar>, 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.

• 出版日期2011-1-15
• 单位中南民族大学; 华中师范大学