二阶奇异非线性微分方程边值问题的正解

Positive Solutions of Boundary Value Problems for Second Order Singular Nonlinear Differential Equations

分别在0≤f+0 <M1,m1<f- ∞ ≤∞和 0 ≤f+∞ <M1,m1<f- 0 ≤∞的情形下研究了非线性奇异边值问题u″+g(t)f(u) =0 ,0 <t <1,αu( 0 ) - βu′( 0 ) =0 ,γu( 1) +δu′( 1) =0 正解的存在性 ,其中f +0 =limu→ 0 f(u) /u ,f- ∞ =limu→∞f(u) /u ,f- 0 =limu→ 0 f(u) /u ,f +∞=limu→∞f(u) /u ,g在区间 [0 。

New existence results are presented for the singular second order nonlinear boundary value problems u″+g(t)f(u)=0,0<t<1,αu(0)-βu′(0)=0,γu(1)+δu′(1)=0 under the conditions 0≤f + 0<M 1, m 1<f - ∞≤∞ or 0≤f + ∞<M 1, m 1<f - 0≤∞, where f + 0= lim u→0 f(u)/u,f - ∞= lim u→∞ f(u)/u, f - 0= lim u→0 f(u)/u, f + ∞= lim u→∞ f(u)/u, g may be singular at t=0 and/or t=1. The proof uses a fixed point theorem in cone theory.