一类奇异的三阶三点非齐次边值问题的正解

Positive solutions for a class of third order three point nonhomogeneous boundary value problems

研究了一类奇异的三阶非线性常微分方程三点非齐次边值问题.运用不动点指数理论,在适当假设下,证明了当非线性项f为超线性时,该问题对小的正参数b至少有一个正解,当b足够大时,该问题没有正解;而当f为次线性时,该问题对所有的正参数b都有正解.

A class of singular third order nonlinear ordinary differential equations with three point nonhomogeneous boundary value conditions were investigated. By using the fixed point index theory and under suitable hypothesis, it was shown that when the nonlinearity f is superlinear, the problem has at least one solution if the parameter b is small enough, and the problem has no positive solution if b is large enough. When f is sublinear, the problem has at least one positive solution for every b 〉 0.