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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.

MSC:
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
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References:
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