Second order BVPs with state dependent impulses via lower and upper functions |
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Authors: | Irena Rachůnková Jan Tomeček |
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Institution: | 1. Department of Mathematical Analysis, and Applications of Mathematics, Faculty of Science, Palacky University, 17. listopadu 12, Olomouc, 771 46, Czech Republic
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Abstract: | The paper deals with the following second order Dirichlet boundary value problem with p ∈ ? state-dependent impulses: z″(t) = f (t,z(t)) for a.e. t ∈ 0, T], z(0) = z(T) = 0, z′(τ i +) ? z′(τ i ?) = I i (τ i , z(τ i )), τ i = γ i (z(τ i )), i = 1,..., p. Solvability of this problem is proved under the assumption that there exists a well-ordered couple of lower and upper functions to the corresponding Dirichlet problem without impulses. |
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