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On existence and multiplicity of positive solutions to periodic boundary value problems for singular nonlinear second order differential equations. (English) Zbl 1030.34024

Summary: The existence and multiplicity of positive solutions are established to periodic boundary value problems for singular nonlinear second-order ordinary differential equations. The arguments are based only upon the positivity of Green’s functions and the Krasnosel’skii fixed-point theorem. As an example, a periodic boundary value problem is also considered which comes from the theory of nonlinear elasticity.

MSC:

34B18 Positive solutions to nonlinear boundary value problems for ordinary differential equations
34B16 Singular nonlinear boundary value problems for ordinary differential equations
74B20 Nonlinear elasticity
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