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

Abstract

We will study the existence of constant sign solutions for the second-order m-point boundary-value problem $$displaylines{ u''(t)+f(t,u(t))=0,quad tin(0,1),cr u(0)=0, quad u(1)=sum^{m-2}_{i=1}alpha_i u(eta_i), }$$ where $mgeq3$, $eta_iin(0,1)$ 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.

Keywords

• Constant sign solutions
• eigenvalue
• bifurcation methods