一类三阶周期边值问题正解的存在性

Existence of Positive Solutions for a Class of Third-Order Periodic Boundary Value Problems

用锥拉伸压缩不动点定理,研究一类三阶常微分方程周期边值问题■正解的存在性,其中α,β,γ均为正的常数,且α∈(0,+∞),β∈(0,π^(2)),γ=αβ,f∈C([0,1]×[0,∞),[0,∞)).结果表明,当非线性项f满足适当的条件时,上述问题至少存在一个正解.

By using the fixed point theorem on expansion and compression of cones,we study the existence of positive solutions for a class of periodic boundary value problems of third-order ordinary differential equations ■,whereα,β,γare positive constants,α∈(0,+∞),β∈(0,π^(2)),γ=αβ,f∈C([0,1]×[0,∞),[0,∞)).The results show that there exists at least one positive solution to the above problem when the nonlinear term f satisfies appropriate conditions.