一类带参数的四阶两点边值问题的多解性

Existence and multiplicity of solutions for a class of fourth-order twopoint boundary value problems with parameters

研究一类带参数的四阶两点边值问题{u^(4)(t)+βu″(t)-αu(t)=f(t,u(t)),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)这里参数α,β∈R且α≥-β^2/4,β<2π^2,α/π^4+β/π^2<1。在非线性项f满足一定的条件下,运用Leggett-Williams不动点定理,获得所讨论问题至少三个非负解的存在性结果。

A class of fourth-order two-point boundary value problems with parameters{u(4)(t)+βu″(t)-αu(t)=f(t,u(t)),t∈(0,1)u(0)=u(1)=u″(0)=u″(1)are studied,where the parametersα,β∈R and α≥-β2/4,β<2/π^2,α/π^4+β/π^2<1.Under certain conditions of the nonlinear term f,the existence of at least three non-negative solutions for the discussed problem are obtained by using fixed point results of Leggett-Williams type.