Electron. J. Diff. Equ., Vol. 2013 (2013), No. 65, pp. 1-7.

Constant sign solutions for second-order m-point boundary-value problems

Jingping Yang

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 5, 2013.
Math Subject Classifications: 34B18, 34C25.
Key Words: Constant sign solutions; eigenvalue; bifurcation methods.

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Jingping Yang
Gansu Institute of Political Science and Law
Lanzhou, 730070, China
email: fuj09@lzu.cn

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