标题： 具有变号权函数的非齐次拟线性椭圆系统两个非平凡解 显示英文标题

标题： Two nontrivial solutions for a nonhomogeneous quasilinear elliptic system with sign-changing weight functions

摘要： 我们感兴趣的是寻找一类具有变号权函数和凹凸非线性项的非齐次拟线性椭圆系统的两个非平凡解，该系统定义在有界区域上。 这类拟线性椭圆系统源于非线性光学，其特点是微分算子不仅依赖于 $\nabla u$ 而且还依赖于 $u$。 利用山路定理和埃凯兰变分原理作为主要工具，我们证明了该系统分别存在一个正能量的非平凡解和一个负能量的非平凡解。 显示英文摘要

摘要： We are interested in looking for two nontrivial solutions for a class of nonhomogeneous quasilinear elliptic system with sign-changing weight functions and concave-convex nonlinearities on the bounded domain. This kind of quasilinear elliptic system arises from nonlinear optics, whose feature is that its differential operator depends on not only $\nabla u$ but also $u$. Employing the mountain pass theorem and Ekeland's variational principle as the major tools, we show that the system has at least one nontrivial solution of positive energy and one nontrivial solution of negative energy, respectively.