科研之友
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摘要
In this paper, we are concerned with the following problem: {(-Delta)(k)u = lambda f(x)vertical bar u vertical bar(q-2)u + g(x)vertical bar u vertical bar(k*-2)u, x is an element of Omega, u is an element of H-0(k)(Omega), where Omega is a bounded domain in R-N with N >= 2k + 1, 1 < q < 2, lambda > 0, f, g are continuous functions on Omega which are somewhere positive but which may change sign on Omega. k(*) = 2N/N-2k is the critical Sobolev exponent. By extracting the Palais-Smale sequence in the Nehari manifold, the existence of multiple nontrivial solutions to this equation is verified.
