带凹凸非线性Kadomtsev-Petviashvili方程解的存在性

The Existence of Solutions to the Kadomtsev-Petviashvili Equation with Concave-convex Nonlinearity

简要介绍Kadomtsev-Petviashvili方程解的研究现状,运用变分方法研究带凹凸非线性Kadomtsev-Petviashvili方程解的存在性。借助Nehari流形可以得到在R^(N)中,方程至少有一个非平凡解。

This paper briefly introduces the research status of solutions to Kadomtsev-Petviashvili equation,and studies the existence of solutions of Kadomtsev-Petviashvili equation with concave-convex nonlinearity by using variational method.With the help of Nehari manifold,it can be obtained that the equation has at least one nontrivial solution in R^(N).