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

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.