带对数非线性项的p-Laplacian型方程的多解性  

Multiple Solutions of p-Laplacian Equations with the Logarithmic Nonlinearity

作　　者：贾文艳 王淑丽 郭祖记 JIA Wen-yan;WANG Shu-li;GUO Zu ji(College of Mathematics,Taiyuan University of Technology,Taiyuan 030024,China)

机构地区：[1]太原理工大学数学学院,山西太原030024

出　　处：《中北大学学报（自然科学版）》2019年第1期26-33,共8页Journal of North University of China(Natural Science Edition)

基　　金：国家自然科学青年基金资助项目(11601363);山西省自然科学基金资助项目(201601D102001)

摘　　要：运用变分法、Nehari流形和对数Sobolev不等式研究了一类带有变号对数非线性项的p-Laplacian型方程解的多重性.将Nehari流形N分成三部分N+,N-和N0,分别讨论了其子流形N+和N-上极小化序列的有界性,证明了极小化序列有强收敛的子列,进而得到该问题至少有两个非平凡解.The multiple solutions of a class of p-Laplacian equations with the sign-changing logarithmic nonlinearity was considered by using variational methods,Nehari manifold and logarithmic Sobolev inequality.The Nehari manifold was divided into three parts:N+,N-and N0.And then the boundedness of the minimizing sequences on the submanifolds N+and N-of the Nehari manifold was respectively discussed.Finally,it was proved that the minimizing sequences contain the strongly convergent subsequences,so two nontrivial solutions of the problem were obtained.

关 键 词：对数非线性项 NEHARI流形 对数SOBOLEV不等式 非平凡解 P-Laplacian型方程 

分 类 号：O177.91[理学—数学]