一类多点边值问题的可解性

This paper deals with the existence of solutions for the problem
{（Фp（u′））′=f（t,u,u′）,t∈（0,1）,
u′（0）=0,u（1）=∑i=1^n-2aiu（ηi）,
where Фp（s）=｜s｜^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai（i=1,2,…,n-2）are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory.

Solvability of Multi-Point Boundary Value Problem

This paper deals with the existence of solutions for the problem $$\left\{\begin{array}{l}(\phi_p(u'))'=f(t,u,u'),\ \ t \in (0,1),\\ u'(0)=0,\ \ u(1)=\sum_{i=1}^{n-2}a_iu(\eta_i),\end{array}\right.$$ where $\phi_p(s)=|s|^{p-2}s,\ p>1$. $0<\eta_1<\eta_2<\cdots<\eta_{n-2}<1,a_i~(i=1,2,\ldots,n-2)$ are non-negative constants and $\sum_{i=1}^{n-2}a_i=1$. Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory.