Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904414 | Acta Mathematica Scientia | 2018 | 22 Pages |
Abstract
In this article, the following concave and convex nonlinearities elliptic equations involving critical growth is considered,
{-Îu=g(x)|u|2*-2u+λf(x)|u|q-2u,xâΩu=0,xââΩ,where Ω â
RN (N ⥠3) is an open bounded domain with smooth boundary, 1 < q < 2,λ > 0.
2*=2NN-2 is the critical Sobolev exponent,
fâL2*2*-q(Ω) is nonzero and nonnegative, and g â C
(Ω¯) is a positive function with k local maximum points. By the Nehari method and variational method, k + 1 positive solutions are obtained. Our results complement and optimize the previous work by Lin [MR2870946, Nonlinear Anal. 75(2012) 2660-2671].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Jiafeng LIAO, Yang PU, Chunlei TANG,