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Bifurcation of branches of solutions for impulsive boundary value problems. (English) Zbl 1438.34112

Summary: This work is concerned with an impulsive boundary value problem for second order differential equations with real parameter. Our approach is based on the implicit function theorem to prove the existence of a unique branches of solutions, moreover we use Krasnosel’skii’s theorem to prove the existence of multiple branches of solutions depending on the values of the real parameter.

MSC:

34B37 Boundary value problems with impulses for ordinary differential equations
34B08 Parameter dependent boundary value problems for ordinary differential equations
34B15 Nonlinear boundary value problems for ordinary differential equations
34C23 Bifurcation theory for ordinary differential equations
34B09 Boundary eigenvalue problems for ordinary differential equations
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References:

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