一类临界拟线性椭圆型方程组解的存在性

Existence Results for a Class of Critical Quasilinear Elliptic Systems

本文讨论了一类临界拟线性椭圆型方程组解的存在性问题.利用LionsPL提出的第二集中紧性原理和山路引理,证明了该方程组在超线性扰动情形下非平凡解的存在性.此外,利用极值原理,也得到了该方程组在次线性扰动情形存在非平凡解.

In this paper,a class of quasilinear elliptic systems with critical nonlinearity is investigated.Using concentrated compactness method and Mountain Pass Lemma,we prove the existence of nontrivial solutions under superlinear perturbation case.Furthermore,we also obtain the existence of nontrivial solutions under the sublinear perturbation by means of extremal principles.