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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.

MSC:

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
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