×

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
PDF BibTeX XML Cite
Full Text: DOI