, Volume 22, Issue 5, pp 1269–1279 | Cite as

Existence of positive solutions for periodic boundary value problem with sign-changing Green’s function

  • D. D. HaiEmail author


We prove the existence of positive solutions for the boundary value problem
$$\begin{aligned} \left\{ \begin{array}{ll} y^{\prime \prime }+m^{2}y=\lambda g(t)f(y), &{}\quad 0\le t\le 2\pi , \\ y(0)=y(2\pi ), &{}\quad y^{\prime }(0)=y^{\prime }(2\pi ), \end{array} \right. \end{aligned}$$
for certain range of the parameter \(\lambda >0\), where \(m\in (1/2,1/2+\varepsilon )\) with \(\varepsilon >0\) small, and f is superlinear or sublinear at \(\infty \) with no sign-conditions at 0 assumed.


Periodic BVP Sign changing Green’s function Positive solutions 

Mathematics Subject Classification

34B15 34B27 


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsMississippi State UniversityMississippi StateUSA

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