摘要
运用变分方法和山路引理研究一类含临界项的Kirchhoff型方程在Neumann边界条件下解的存在性.首先,通过方程对应的能量泛函及解的定义获得平凡解的等价条件;其次,考虑Kirchhoff方程的特征问题,并利用反证法与Brezis-Lieb′s引理证明能量泛函满足PS条件;最后,根据山路引理得到泛函的临界值,然而其临界点就是该方程的解.
The variational method and mountain lemma are used to study the existence of solutions for a class of Kirchhoff type equations with critical terms under Neumann boundary conditions.First,the equivalent conditions of trivial solutions are obtained through the corresponding energy functionals of the equations and the definition of the solutions.Second,considering the characteristic problem of the Kirchhoff equation,the contradiction method and Brezis-Lieb′s lemma are used to prove that the energy functional satisfies the PS condition.Finally,the critical value of the functional is obtained according to the mountain lemma,but its critical point is the solution of the equation.
作者
叶红艳
索洪敏
李伟
袁恋
YE Hongyan;SUO Hongmin;LI Wei;YUAN Lian(School of Data Science and Information Engineering,Guizhou Minzu University,Guiyang 550025,China)
出处
《湖北民族大学学报（自然科学版）》
CAS
2020年第2期194-199,共6页
Journal of Hubei Minzu University:Natural Science Edition
基金
国家自然科学基金项目(11661021,11861021)
贵州省教育厅基金项目(黔教合KY字[2016]163,KY字[2016]029,黔教合基础[2019]1163).
