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Second order BVPs with state dependent impulses via lower and upper functions

100%
Rachůnková I., Tomeček J.
Open Mathematics
|
2014
|
tom 12
|
nr 1
128-140
EN
The paper deals with the following second order Dirichlet boundary value problem with p ∈ ℕ 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.
2
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On variational impulsive boundary value problems

100%
Galewski M.
Open Mathematics
|
2012
|
tom 10
|
nr 6
1969-1980
EN
Using the variational approach, we investigate the existence of solutions and their dependence on functional parameters for classical solutions to the second order impulsive boundary value Dirichlet problems with L1 right hand side.
3
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Mild solution of fractional order differential equations with not instantaneous impulses

76%
Li P.-L., Xu C.-J.
Open Mathematics
|
2015
|
tom 13
|
nr 1
EN
In this paper, we investigate the boundary value problems of fractional order differential equations with not instantaneous impulse. By some fixed-point theorems, the existence results of mild solution are established. At last, one example is also given to illustrate the results.
4
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Existence of mild solutions for semilinear differential equations with nonlocal and impulsive conditions

64%
Olszowy L.
Open Mathematics
|
2014
|
tom 12
|
nr 4
623-635
EN
This paper is concerned with the existence of mild solutions for impulsive semilinear differential equations with nonlocal conditions. Using the technique of measures of noncompactness in Banach and Fréchet spaces of piecewise continuous functions, existence results are obtained both on bounded and unbounded intervals, when the impulsive functions and the nonlocal item are not compact in the space of piecewise continuous functions but they are continuous and Lipschitzian with respect to some measure of noncompactness, and the linear part generates only a strongly continuous evolution system.
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