POSITIVE SOLUTIONS FOR SECOND ORDER INTEGRAL BOUNDARY VALUE PROBLEMS WITH SIGN-CHANGING NONLINEARITIES - Zou, Y. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
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.