关于一类带有非线性边界条件的拟线性椭圆方程(英文)

On a Class of Quasilinear Elliptic Equations with Nonlinear Boundary Condition

本文研究了一类带有非线性边界条件的拟线性椭圆方程.在比常用的经典条件弱的假设条件下,得到该方程所对应的能量泛函存在有界Palais-Smale序列.然后,利用山路引理,得到该方程非平凡解的存在性.最后,给出一个例子,说明所给的条件比经典条件弱.

In this paper, we investigate a class of quasilinear elliptic equations with nonlinear boundary condition. The existence of bounded Palais-Smale sequences for the corresponding functional of the equation is obtained under hypotheses weaker than those commonly used in the literature. Then, by applying Mountain Pass Lemma, the existence of nontrivial solution is confirmed. Furthermore, we give an example which illustrates that the condition we give is more general than the superquadratic growth condition.