Electronic Journal of Differential Equations,
Vol. 2013 (2013), No. 65, pp. 1-7.
Title: Constant sign solutions for second-order m-point boundary-value problems
Author: Jingping Yang (Gansu Inst. of Political Science and Law, Lanzhou, China)
Abstract:
We will study the existence of constant sign solutions for the second-order
m-point boundary-value problem
$$\displaylines{
u''(t)+f(t,u(t))=0,\quad t\in(0,1),\cr
u(0)=0, \quad u(1)=\sum^{m-2}_{i=1}\alpha_i u(\eta_i),
}$$
where $m\geq3$, $\eta_i\in(0,1)$ and $\alpha_i>0$ for
$i=1,\dots,m-2$, with $\sum^{m-2}_{i=1}\alpha_i<1$, we obtain that
there exist at least a positive and a negative
solution for the above problem. Our approach is based on
unilateral global bifurcation theorem.
Submitted November 8, 2012. Published March 05, 2013.
Math Subject Classifications: 34B18, 34C25.
Key Words: Constant sign solutions; eigenvalue; bifurcation methods.