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Second order nonlinear differential equations with linear impulse and periodic boundary conditions

Aydin Huseynov — 2011

Applications of Mathematics

In this study, we establish existence and uniqueness theorems for solutions of second order nonlinear differential equations on a finite interval subject to linear impulse conditions and periodic boundary conditions. The results obtained yield periodic solutions of the corresponding periodic impulsive nonlinear differential equation on the whole real axis.

On positive solutions for a nonlinear boundary value problem with impulse

Huseyin Bereketoglu;  Aydin Huseynov — 2006

Czechoslovak Mathematical Journal

In this paper we study nonlinear second order differential equations subject to separated linear boundary conditions and to linear impulse conditions. Sign properties of an associated Green’s function are investigated and existence results for positive solutions of the nonlinear boundary value problem with impulse are established. Upper and lower bounds for positive solutions are also given.

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