具有变号非线性项的拟线性椭圆方程多解的存在性

Existence of Multiple Solutions for a Quasilinear Elliptic Equation with Sign-Changing Nonlinearities

利用山路定理研究了具有Dirichlet边值问题-div(|▽u|^(2p-2)▽u/(1+|▽u|^(2p))^(1/2))=λf(x,u)多解的存在性,且非线性项f可以变号.

We utilize the mountain pass theorem to study the quasilinear elliptic equation —div(|▽u|^(2p-2)▽u/(1+|▽u|^(2p))^(1/2)) = λf(x,u) with Dirichlet boundary condition and obtain the existence result of multiple solutions;furthermore,the nonlinear term / is allowed to be sign-changing.