含有陡哨势阱和凹凸非线性项的Kirchhoff型问题的多重正解

Multiple Positive Solutions for Kirchhoff-Type Problems with Steep Potential Well and Concave-Convex Nonlinearities

在这篇文章中,作者研究涉及凹凸非线性项的Kirchhoff型问题{-(a+b)∫|■u|^(2)dx)△u+λV(x)u=μf(x)|u|^(q-2)u+|u|^(p-2)u,x∈R^(3),u∈H^(1)R^(3),其中a,b>0是常数,λ,μ>0是参数,l<q<2,4<p<6且V是一个非负连续位势.在f(x)和V的合适条件下,此问题正解的存在性和集中性能够通过Nehari流形和Ekeland变分原理得到.

In this paper,the authors research the following Kirchhoff type problem involving concave-convex nonlinearities{-(a+b)∫|■u|^(2)dx)△u+λV(x)u=μf(x)|u|^(q-2)u+|u|^(p-2)u,x∈R^(3),u∈H^(1)R^(3),where a,b>0 are cons tants,λ,μ>0 are parameters,1<q<2,4<p<6 and V is a nonnegative continuous potential.Under some suitable assumptions on and V,the existence and concentration of positive solutions to this problem are obtained by using Nehari manifold and Ekeland variational principle.