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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 $$\aligned &-u'' = f(t,u,u'), \quad t \in (0,1), t \ne t_k,\\ &\triangle u(t_k) = I_k(u(t_k)), -\triangle u'(t_k) = N_k(u(t_k)), \quad k = 1,\ldots,m,\\ &au(0) - bu'(0) = 0, \quad cu(1) + du'(1) = 0, \endaligned $$ where $0 < t_1 < \ldots < t_m < 1$, 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.

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