四阶两参数共振边值问题的可解性

Solvability of a Fourth-order Boundary Value Problem at Resonance

运用Leray Schauder原理 ,在共振条件下 ,讨论了一类四阶两参数非线性常微分方程的边值问题 .在允许非线性项跨越特征线扰动的条件下 。

By using Leray Schauder Theorem, a class of nonlinear fourth order boundary value problem with two parameters is studied at resonance. It is showed that the problem has at least one solution when the asymptotic values of u -1 g (x,u) cross infinitely many eigenlines.