一类带不定权拟线性椭圆方程组的解

Solutions for a System of Quasilinear Elliptic Equations with Indefinite Weights

利用临界点理论中的山路引理,讨论一类带不定权拟线性椭圆方程组的Dirichlet问题.借助相应带不定权特征值问题的第一特征值建立了其非平凡解的存在性定理,其中方程组中特征值参数小于某已知常数.

In this paper, the Dirichlet problem of a class of quasilinear elliptic systems with indefinite weights, which comes from mathematical models of Non Newton fluid flow, population evolution, pattern (formation) etc, is discussed by using Mountain Pass Lemma in critical point theory. The existence of a nontrivial weak solution is established with the help of the first eigenvalue of the corresponding eigenvalue problem, where the eigenvalue parameter is less than a known constant.