中北大学学报（自然科学版）2017，Vol.38Issue(6)：576-581,6.DOI:10.3969/j.issn.1673-3193.2017.06.004
含次临界Sobolev指数半线性合作椭圆方程组非平凡解的存在性
Existence of Nontrivial Solutions of the Semilinear Cooperative Elliptic Systems Involving Subcritical Sobolev Exponents
摘要
Abstract
One cooperative semilinear elliptic systems involving subcritical Sobolev exponents was inves-tigated.The existence of nontrivial solution to the systems was obtained under different cases.In the case 0<λ<λ1 ,through defining the functional and the corresponding Nehari manifold,we got that the functional J (u,v)was bounded below.Then it proved that the functional had a minimizer,so the func-tional had a nontrivial critical point in the Nehari manifold and the problem had a nontrivial solution in E .In the caseλk <λ<λk+1 ,the functional satisfied the conditions of local linking theorem.It draws the conclusion that there exists at least one nontrivial solution.关键词
次临界Sobolev指数/合作椭圆方程组/Nehari流形/局部环绕定理Key words
subcritical Sobolev exponents/cooperative elliptic systems/Nehari manifold/local linking theorem分类
数理科学引用本文复制引用
樊自安,寇继生..含次临界Sobolev指数半线性合作椭圆方程组非平凡解的存在性[J].中北大学学报（自然科学版）,2017,38(6):576-581,6.基金项目
国家自然科学基金资助项目(11301163) （11301163）
湖北省教育厅科学研究计划项目(B2015032) （B2015032）
