一类带参数的四阶两点边值问题的多解性

Multiplicity of solutions for a class of fourth-order two-point boundary value problems with parameters

研究一类带两个参数的四阶两点边值问题,在非线性项f满足一定条件时,运用Leggett-Williams不动点定理获得了该问题至少两个正解的存在性结果.最后通过3个例子说明了所获结果的有效性.

When nonlinear term satisfies certain conditions,the existence of at least two positive solutions is discussed for a class of fourth-order two-point boundary value problems with two parameters by means of Leggett-Williams fixed point theorem.Finally,three models are given to verify the effectiveness of the obtained results.