一类p(x)-Laplacian方程组解的存在性

Existence of solutions to a class of p(x)-Laplacian equations

在W01,p(x)(Ω)×W01,q(x)(Ω)空间框架下研究具有p(x)增长条件的椭圆形偏微分方程组。通过讨论相应的泛函的临界点的存在性,得到偏微分方程组弱解的存在性,推广了在Sobolev空间中弱解的相应结论。

This paper studies the elliptic partial differential equations satisfying p （x） growth conditions in the setting of X=W0^1,p（x）（Ω）×W0^1,q（x）（Ω） space. The discussion of the existence of the critical point to the corresponding functional results in the existence of weak solutions , which generalizes the corresponding work for the weak solutions in Sobolev space.