带第一特征值的具临界指数的拟线性椭圆方程非平凡弱解存在的一个必要条件

A necessary condition on existence of non-trivial weak solutionfor the quasi-linear equation with the first eigenvalue,involving the critical Sobolev exponents

建立了一类带第一特征值λ1的具临界指数的拟线性椭圆方程 零边值问题的非平凡弱解存在的一个必要条件.

In this paper, a necessary condition on existence of non-trivial solution for the quasi-linear equations （-△pμ=λ1|μ|p-2μ+|μ|p-2μ）with the first eigenvalue (λ1)of the p-Laplacian, involving the critical Sobolev exponents, was given.