On a superlinear periodic boundary value problem with vanishing Green's function

Abstract

We prove the existence of positive solutions for the boundary value problem \[ \begin{cases} y^{\prime \prime }+a(t)y=\lambda g(t)f(y),\quad 0\leq t\leq 2\pi, \\ y(0)=y(2\pi ),\quad y^{\prime }(0)=y^{\prime }(2\pi ), \end{cases} \] where $\lambda $ is a positive parameter, $f$ is superlinear at $\infty$ and could change sign, and the associated Green's function may have zeros.

Keywords

• superlinear
• periodic
• vanishing green's function