一类p-双调和方程的Berestycki-Lions结果  

A Berestycki-Lions Type Result for A Class of P-biharmonic Equation

作　　者：陶钬 李麟[1] TAO Huo;LI Lin(School of Mathematics and Statistics,Chongqing Technology and Business University,Chongqing 400067,China)

机构地区：[1]重庆工商大学数学与统计学院,重庆400067

出　　处：《西华师范大学学报（自然科学版）》2024年第3期261-266,共6页Journal of China West Normal University(Natural Sciences)

基　　金：国家自然科学基金项目(11861046);重庆市教育委员会基金项目(KJQN20190081);重庆工商大学基金项目(CTBUZDPTTD201909)。

摘　　要：本文研究了一个带有p-双调和算子的拟线性椭圆方程的Beresticki-Lions型问题。首先,给出方程对应的Pohozaev恒等式;其次,给出对应的辅助方程,且利用变分法证明辅助方程解的存在性;最后,利用单调性技巧、Palais对称临界原理和变分法,证明了原问题非平凡解的存在性。该结果完善了p-双调和方程解的存在性结果,并给出这类问题新的可解性条件。A Berestycki-Lions type problem for a quasilinear elliptic equation involving the p-biharmonic operator is considered in this paper.Firstly,the Pohozaev identity corresponding to the equation is given.Secondly,the corresponding auxiliary equation is provided,and the existence of solution to the auxiliary equation is proved by the variational method.Finally,the existence of nontrivial solution for the original problem is demonstrated by the monotonicity technique,Palais symmetric criticality principle and variational method.The result has improved the existence of solution for the p-biharmonic equation.Moreover,a new solvable condition for this equation is presented.

关 键 词：p-双调和算子 POHOZAEV恒等式 Berestycki-Lions条件 椭圆方程 变分法 

分 类 号：O175[理学—数学]