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

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 $\in...

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Bibliographic Details
Published in:Electronic journal of qualitative theory of differential equations 2016-01, Vol.2016 (55), p.1-12
Main Author: Hai, Dang Dinh
Format: Article
Language:English
Subjects:
periodic
superlinear
vanishing green's function
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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.
ISSN:1417-3875
1417-3875
DOI:10.14232/ejqtde.2016.1.55