Positive solutions and eigenvalues of nonlocal boundary-value problems

Abstract

We study the ordinary differential equation $x''+lambda a(t)f(x)=0$ with the boundary conditions $x(0)=0$ and $x'(1)=int_{eta}^{1}x'(s)dg(s)$. We characterize values of $lambda$ for which boundary-value problem has a positive solution. Also we find appropriate intervals for $lambda$ so that there are two positive solutions.

Keywords

• Nonlocal boundary-value problems
• Positive solutions
• eigenvalues
• fixed point theorem in cones.