带有临界增长的Kirchhoff方程极小能量变号解的存在性  

Existence of least energy sign-changing solutions to Kirchhoff equation with critical growth

作　　者：梁文国 黄永艳[1] LIANG Wenguo;HUANG Yongyan(School of Mathematical Sciences,Shanxi University,Taiyuan,Shanxi 030006,China)

机构地区：[1]山西大学数学科学学院,山西太原030006

出　　处：《河北科技大学学报》2020年第4期327-333,共7页Journal of Hebei University of Science and Technology

基　　金：国家自然科学基金(11671239,11701346,11801338)。

摘　　要：为了深入研究Kirchhoff方程的性质,讨论了带有Hartree项和临界增长非线性项的Kirchhoff方程极小能量变号解的存在性。利用能量泛函在变号Nehari流形上的下确界Cλ收敛于0,得到空间E紧嵌入L 6(R 3)这一技术性结果。结果表明,利用限制变分方法和定量形变引理获得极小化序列对应的极小值点是该问题的非平凡解。研究方法在理论证明方面得到了良好的结果,对研究其他Kirchhoff方程解的存在性有一定的指导意义。In order to deeply study the characteristics of Kirchhoff equation,the existence result of the least energy sign-changing solutions to Kirchhoff equation with Hartree term and critical growth nonlinear term was discussed.The technical result of the space E compact embedding L 6(R 3)was obtained by using the infimum of the energy functional on the sign-changing Nehari manifold convergences to zero.The results shows that the minimum point corresponding to the minimizing sequence obtained by the restricted variational method and quantitative deformation lemma is the nontrivial solutions for the problem.The research method in theoretical proof gets effective results and has a certain guiding significance for studying the existence of solutions of other Kirchhoff equations.

关 键 词：非线性泛函分析 KIRCHHOFF方程 Hartree非线性项 临界增长 变分方法 变号解 

分 类 号：O175[理学—数学]