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Multiplicity of solutions to two-point boundary value problems for second-order impulsive differential equations. (English) Zbl 1165.34329

The authors consider the impulsive boundary value problem

-u '' =f(t,u,u ' ),t(0,1),tt k ,u(t k )=I k (u(t k )),-u ' (t k )=N k (u(t k )),k=1,...,m,au(0)-bu ' (0)=0,cu(1)+du ' (1)=0,

where 0<t 1 <...<t m <1, the functions f, I k , N k are continuous. Sufficient conditions for the existence of at least three solutions are obtained. Main results are proved by using lower and upper solutions and Leray-Schauder degree theory.

MSC:
34B37Boundary value problems for ODE with impulses
47N20Applications of operator theory to differential and integral equations
34B15Nonlinear boundary value problems for ODE