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1
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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
Content available remote

Existence theory for sequential fractional differential equations with anti-periodic type boundary conditions

76%
Aqlan M. H., Alsaedi A., Ahmad B., Nieto J. J.
Open Mathematics
|
2016
|
tom 14
|
nr 1
723-735
EN
We develop the existence theory for sequential fractional differential equations involving Liouville-Caputo fractional derivative equipped with anti-periodic type (non-separated) and nonlocal integral boundary conditions. Several existence criteria depending on the nonlinearity involved in the problems are presented by means of a variety of tools of the fixed point theory. The applicability of the results is shown with the aid of examples. Our results are not only new in the given configuration but also yield some new special cases for specific choices of parameters involved in the problems.
3
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Two-point boundary value problems for the generalized Bagley-Torvik fractional differential equation

76%
Staněk S.
Open Mathematics
|
2013
|
tom 11
|
nr 3
574-593
EN
We investigate the fractional differential equation u″ + A c D α u = f(t, u, c D μ u, u′) subject to the boundary conditions u′(0) = 0, u(T)+au′(T) = 0. Here α ∈ (1, 2), µ ∈ (0, 1), f is a Carathéodory function and c D is the Caputo fractional derivative. Existence and uniqueness results for the problem are given. The existence results are proved by the nonlinear Leray-Schauder alternative. We discuss the existence of positive and negative solutions to the problem and properties of their derivatives.
4
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Three solutions to discrete anisotropic problems with two parameters

76%
Galewski M., Kowalski P.
Open Mathematics
|
2014
|
tom 12
|
nr 10
1403-1415
EN
In this note we derive a type of a three critical point theorem which we further apply to investigate the multiplicity of solutions to discrete anisotropic problems with two parameters.
5
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Positivity conditions and bounds for Green’s functions for higher order two-point BVP

76%
Gil’ M.
Open Mathematics
|
2011
|
tom 9
|
nr 5
1156-1163
EN
We consider a linear nonautonomous higher order ordinary differential equation and establish the positivity conditions and two-sided bounds for Green’s function for the two-point boundary value problem. Applications of the obtained results to nonlinear equations are also discussed.
6
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Nonlinear Leray-Schauder alternatives and application to nonlinear problem arising in the theory of growing cell population

64%
Amar A.
Open Mathematics
|
2011
|
tom 9
|
nr 4
851-865
EN
Motivated by a mathematical model of an age structured proliferating cell population, we state some new variants of Leray-Schauder type fixed point theorems for (ws)-compact operators. Further, we apply our results to establish some new existence and locality principles for nonlinear boundary value problem arising in the theory of growing cell population in L 1-setting. Besides, a topological structure of the set of solutions is provided.
7
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Integrable three-dimensional coupled nonlinear dynamical systems related to centrally extended operator Lie algebras and their Lax type three-linearization

64%
Golenia J., Hentosh O., Prykarpatsky A.
Open Mathematics
|
2007
|
tom 5
|
nr 1
84-104
EN
The Hamiltonian representation for a hierarchy of Lax type equations on a dual space to the Lie algebra of integro-differential operators with matrix coefficients, extended by evolutions for eigenfunctions and adjoint eigenfunctions of the corresponding spectral problems, is obtained via some special Bäcklund transformation. The connection of this hierarchy with integrable by Lax two-dimensional Davey-Stewartson type systems is studied.
8
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Triple solutions for a Dirichlet boundary value problem involving a perturbed discretep(k)-Laplacian operator

64%
Khaleghi Moghadam M., Henderson J.
Open Mathematics
|
2017
|
tom 15
|
nr 1
1075-1089
EN
Triple solutions are obtained for a discrete problem involving a nonlinearly perturbed one-dimensional p(k)-Laplacian operator and satisfying Dirichlet boundary conditions. The methods for existence rely on a Ricceri-local minimum theorem for differentiable functionals. Several examples are included to illustrate the main results.
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