中北大学学报（自然科学版）2018，Vol.39Issue(2)：107-113,7.DOI:10.3969/j.issn.1673-3193.2018.02.001
带有临界指数的p-Kirchhoff型方程正基态解的存在性
Existence of Positive Ground State Solutions for p-Kirchhoff Type Equations with Critical Exponents
摘要
Abstract
Existence of positive ground state solutions for p-Kirchhoff type equations with critical expo-nents on RN was investigated by using variational methods.First,it was proved that energy functional corresponding to the problem possessed the geometric structure of the mountain pass theorem.Moreo-ver,by using the Ekeland variational principle,a (PS)c sequence,satisfying asymptotic property G(un)=o(1) of combining Nehari mainfold with Pohozaev's identity,was obtained.Second,it was proved that the (PS)c sequence was bounded and it was proved that c<c? by the implicit function theo-rem.Finally,it was proved that the sequence possessed a strong convergence subsequence.Hence,the equation has a positive ground state solution.关键词
变分法/p-Kirchhoff型方程/正基态解/山路定理/消失引理Key words
variational methods/p-Kirchhoff type equation/positive ground state solution/mountain pass theorem/vanishing lemma分类
数理科学引用本文复制引用
白容宇,王淑丽,郭祖记..带有临界指数的p-Kirchhoff型方程正基态解的存在性[J].中北大学学报（自然科学版）,2018,39(2):107-113,7.基金项目
国家自然科学青年基金资助项目(11601363) （11601363）
山西省自然科学基金资助项目(201601D102001) （201601D102001）
