一类具有组合非线性项的p-Laplace方程的多解性及集中紧性

Multiplicity and concentration of solutions to a class of p-Laplace equations with mixed nonlinearity

该文研究了一类具有组合非线性项的p-Laplace方程的多解性以及解的集中紧性.当位势函数V(x)满足较弱的条件时,利用变分法,得到了该方程多个非平凡解的存在性并讨论了解的集中紧性,所得结果推广了相关文献的研究成果.

In this paper,a class of p-Laplace equations with mixed nonlinearity is studied.When the potential function V(x)satisfies some mild assumptions,the existence of multiple nontrivial solutions of the equation is obtained by using the variational method.Moreover,the concentration of solutions is also explored.The results extend the research results of related literatures.