一类高阶拟线性椭圆方程共振问题的可解性

On the solvability of a higher order bf quasilinear elliptic resonance problem

研究任意特征值的高阶拟线性椭圆方程共振问题,而非线性项为无界函数,且满足超线性增长条件.引入伪特征值的概念,在推广的Landesman-Lazer条件下,得到上述问题解的存在性定理.

The resonance problem of the higher order quasilinear elliptic equation with arbitrary eigenvalue was dealt with, where the unbounded non-linear term satisfied the superlinear condition, and a new notation of psuedo-eigenvalue was introduced. Then, an existence theorem was obtained under the Landesman-Lazer condition.