## On a superlinear periodic boundary value problem with vanishing Green’s function.(English)Zbl 1363.34072

Summary: 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.

### MSC:

 34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations 34B09 Boundary eigenvalue problems for ordinary differential equations 34B15 Nonlinear boundary value problems for ordinary differential equations 34B27 Green’s functions for ordinary differential equations

### Keywords:

superlinear; periodic; vanishing Green’s function
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