Nonexistence of nontrivial weak solutions for anisotropic elliptic problems

Abstract

In this paper, we consider anisotropic elliptic problems on a bounded smooth domain, nonexistence of nontrivial weak solutions are obtained by two different simplified methods. We point out the results of nonexistence of nontrivial weak solutions not only depend on the size and shape of domain, but also the constants   ${p_1}$ and ${p_N}$  in anisotropic elliptic problems.