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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 \(f\in \text{Car}([0,T]\times \mathbb R^+, \mathbb R)\). The existence results are obtained by using a fixed point theorem in cones.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
34B27 Green’s functions for ordinary differential equations
47N20 Applications of operator theory to differential and integral equations
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