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Periodic solutions for second-order differential equations with a singular nonlinearity. (English) Zbl 1162.34316
Summary: This paper deals with the existence of positive $T$-periodic solutions for the following differential equation $$\ddot x +a(t)x= f(t,x)+ c(t),$$ where $a, c\in L^{1}[0,T]$ and $f\in \text{Car}([0,T]\times \Bbb R^+, \Bbb R)$. The existence results are obtained by using a fixed point theorem in cones.

34B18Positive solutions of nonlinear boundary value problems for ODE
34B16Singular nonlinear boundary value problems for ODE
34B27Green functions
47N20Applications of operator theory to differential and integral equations
Full Text: DOI
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