On the existence of more positive solutions of periodic bvps with singularity

Abstract

We consider Periodic boundary value problems for ordinary second order differential equations of the form u′′=f(t,u,u′), Where f satisfies the (local) Carathéodory conditions and can have a singularity in the second variable.Writing our problem in an operator can be computed on. These sets are not convex, in general. Using the degree theory we get at least one fixed point of the operator at each such set which leads to the existence and localization of more solutions of the related Periodic boundary value problem. Our results are based on the generalized lower and upper functions method from Rachůnková and Tvrdý[15].

Keywords:

• Second order nonlinear ordinary differential equation
• Periodic solution
• Topological degree
• Lower and upper functions
• Strong repulsive singularity
• Multiplicity

AMS:

• 34B16
• 34B18
• 34C25

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Notes

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