拟线性滞后型微分方程正解的存在性(英文)

The Existence of Positive Solutions for the Quasilinear Functional Delay Differential Equations

本文研究了下面这种拟线性滞后型微分方程(g(u′)′+a(t) f (ut) =0 , 0 <t<1其中 g(v) =|v|p-2 v,p >1 ,满足非线性边界条件 .并且通过应用锥不动定理与阿尔采拉 -阿斯卡里定理 ,证明了上述方程至少存在一个正解 .

In this paper, we study the existence of positive solutions of the quasilinear functional delay differential equation of the form(g(u′))′+a(t)f(u t)=0, 0<t<1(1)where g(v)=|v| p-2 v, p>1, subject to nonlinear boundary conditions. We show that there exists at least one positive solution by applying a fixed point theorem in cones and the Arzela Ascoli theorem.