一类非局部椭圆方程Navier边值问题弱解的存在性

Existence of Weak Solution for a Class of Nonlocal Elliptic Problem with Navier Boundary

本文主要利用变分法讨论了一类带有非局部项的四阶Navier边值问题弱解的存在性。在对非线性项做适当的假设后,作者利用山路引理证明了该问题至少存在一个非零弱解。

By the variational methods,the present paper considers the existence of solution for a fourth-or- der Navier boundary problem with nonlocal term. Applying the Mountain Pass Theorem, the author proves that the problem has at least one nontrival weak solution under some suitable assumptions.