POSITIVE SOLUTIONS FOR SECOND ORDER INTEGRAL BOUNDARY VALUE PROBLEMS WITH SIGN-CHANGING NONLINEARITIES

Abstract

We prove the existence of positive solutions for the second order integral boundary value problem
$$
\displaystyle
\left\{
\begin{array}{l}
\displaystyle u''(t)+\lambda f(u(t))=0,\ \ t\in (0,1),
\vspace{0.2cm}\\
\displaystyle u(0)=\int_0^1u(s)d\alpha(s),\ \ u(1)=\int_0^1u(s)d\beta(s),
\end{array}
\right.
$$
where $f\in C(\mathbb{R},\mathbb{R})$ is sign-changing.