一类渐近线性双调和方程解的存在性

Existence of solutions for a class of asymptotically linear biharmonic equations

主要研究Dirichlet边界条件下一类双调和方程在开球上解的存在性.与之前许多研究此类问题的文章所不同的是,此时非线性项满足渐近线性条件.本文利用满足Cerami条件的山路定理,得到了非平凡解的存在性.

This paper considers the existence of solutions for a class of biharmonicequations with Dirichlet boundary condition in an open ball. By using Mountain Pass theorem, which satisfies Cerami condition, it proves the existence of non-trivial solutions when the non-linear term satisfies asymptotically linear condition. This is different from other＇s study.