A periodic boundary value problem with vanishing Green’s function. (English) Zbl 1135.34307

Summary: We consider the boundary value problem
\[ \begin{cases} y''+a(t)y=g(t)f(y),\quad & 0\leq t\leq 2\pi,\\ y(0)=y(2\pi),\quad & y'(0)=y'(2\pi),\end{cases} \]
and establish the existence of nonnegative solutions in the case where the associated Green’s function may have zeros. The results are illustrated by an example.


34B15 Nonlinear boundary value problems for ordinary differential equations
34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
Full Text: DOI


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