加权Sobolev空间中奇异拟线性椭圆方程共振问题

Resonance Problem of A Singular Quasilinear Elliptic Equation in Weighted Sobolev Space

通过将拟线性算子M与线性算子L之间建立一种关系,在加权Sobolev空间针对算子M的高阶特征值,利用Galerkin方法、推广的Brouwer定理以及由Shapiro建立的新型加权Sobolev紧嵌入定理,并对非线性项进行合理假设,研究了一类奇异拟线性椭圆方程共振问题,得到其弱解的存在性.

By establishing a relationship between the quasilinear operator and the linear operator ,and making reasonable assumptions about nonlinear terms, the existence of a nontrivial solution for a class of quasilinear elliptic equations with high eigenvalues in a weighted Sobolev space was proved. The proof relies on the Galerkin method, the Brouwer＇s theorem and a new weighted compact Sobolev-type embedding theorem established by Shapiro.