弱半正三阶三点边值问题的正解

The positive solutions are studied for the nonlinear third-order three-point boundary value problem u′″（t）=f（t,u（t））,a.e,t∈0,1],u（0）=u′（η）=u″（1）=0, where the nonlinear term f（t, u） is a Caratheodory function and there exists a nonnegative function h ∈ L^10, 1] such that f（t, u） 〉 ≥-h（t）. The existence of n positive solutions is proved by considering the integrations of ＂height functions＂ and applying the Krasnosel＇skii fixed point theorem on cone.

Positive Solutions of a Weak Semipositone Third-Order Three-Point Boundary Value Problem

The positive solutions are studied for the nonlinear third-order three-point boundary value problem $$\begin{array}{c}u'(t)=f(t,u(t)),~\mbox{a.e.}~t\in 0,1],\quad u(0)=u'(\eta)=u'(1)=0,\end{array}$$where the nonlinear term $f(t,u)$ is a Carath\'eodory function and there exists a nonnegative function $h\in L^{1}0,1]$ such that$f(t,u)\geq -h(t)$. The existence of $n$ positive solutions is proved by considering the integrations of ``height functions' and applying the Krasnosel'skii fixed point theorem on cone.