The Experts below are selected from a list of 1758 Experts worldwide ranked by ideXlab platform
S.k. Ntouyas - One of the best experts on this subject based on the ideXlab platform.
-
Existence Results for Impulsive Semilinear Damped Differential Inclusions
2014Co-Authors: M. Benchohra, S.k. Ntouyas, J. Henderson, A. OuahabAbstract:In this paper we investigate the existence of mild solutions for first and second order impulsive semilinear evolution inclusions in real separable Banach spaces. By using suitable fixed point theorems, we study the case when the Multivalued Map has convex and nonconvex values. Key words and phrases: Impulsive damped differential inclusions, fixed point, semigroup, cosine operators, measurable selections, contraction Map, Banach space
-
existence of solutions for fractional differential inclusions with nonlocal riemann liouville integral boundary conditions
Mathematica Bohemica, 2014Co-Authors: Bashir Ahmad, S.k. NtouyasAbstract:In this paper, we discuss the existence of solutions for a boundary value problem of fractional differential inclusions with nonlocal Riemann-Liouville integral boundary conditions. Our results include the cases when the Multivalued Map involved in the problem is (i) convex valued, (ii) lower semicontinuous with nonempty closed and decomposable values and (iii) nonconvex valued. In case (i) we apply a nonlinear alternative of Leray-Schauder type, in the second case we combine the nonlinear alternative of Leray-Schauder type for single-valued Maps with a selection theorem due to Bressan and Colombo, while in the third case we use a fixed point theorem for Multivalued contractions due to Covitz and Nadler.
-
EXISTENCE RESULTS FOR FIRST ORDER IMPULSIVE SEMILINEAR EVOLUTION INCLUSIONS
2013Co-Authors: M. Benchohra, J. Henderson, S.k. NtouyasAbstract:In this paper the concepts of lower mild and upper mild solutions combined with a fixed point theorem for condensing Maps and the semigroup theory are used to investigate the existence of mild solutions for first order impulsive semilinear evolution inclusions. Key words and phrases: Initial value problem, impulsive differential inclusions, convex Multivalued Map, condensing Map, fixed point, truncation Map, upper mild and lower mild solutions
-
Controllability Results for Semilinear Evolution Inclusions with Nonlocal Conditions
Journal of Optimization Theory and Applications, 2003Co-Authors: M. Benchohra, E.p. Gatsori, S.k. NtouyasAbstract:In this paper, we prove controllabillity results for mild solutions defined on a compact real interval for first-order semilinear differential and integrodifferential evolution inclusions in Banach spaces with nonlocal conditions. By using suitable fixed-point theorems, we study the cases when the Multivalued Map has convex values as well as nonconvex values.
Garik Petrosyan - One of the best experts on this subject based on the ideXlab platform.
-
Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions
Fixed Point Theory and Applications, 2019Co-Authors: Mikhail Kamenskii, Valeri Obukhovskii, Garik Petrosyan, Jen-chih YaoAbstract:We study a semilinear fractional order differential inclusion in a separable Banach space E of the form $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where \({}^{C}D^{q}\) is the Caputo fractional derivative of order \(0 < q < 1\), \(A \colon D(A) \subset E \rightarrow E\) is a generator of a \(C_{0}\)-semigroup, and \(F \colon [0,T] \times E \multiMap E\) is a nonlinear Multivalued Map. By using the method of the generalized translation Multivalued operator and a fixed point theorem for condensing Multivalued Maps, we prove the existence of a mild solution to this inclusion satisfying the nonlocal boundary value condition: $$ x(0)\in \Delta (x), $$ where \(\Delta : C([0,T];E) \multiMap E\) is a given Multivalued Map. The semidiscretization scheme is developed and applied to the approximation of solutions to the considered nonlocal boundary value problem.
-
Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions
Fixed Point Theory and Applications, 2019Co-Authors: Mikhail Kamenskii, V. Obukhovskii, Garik PetrosyanAbstract:We study a semilinear fractional order differential inclusion in a separable Banach space E of the form D q C x ( t ) ∈ A x ( t ) + F ( t , x ( t ) ) , t ∈ [ 0 , T ] , $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where D q C ${}^{C}D^{q}$ is the Caputo fractional derivative of order 0 < q < 1 $0 < q < 1$ , A : D ( A ) ⊂ E → E $A \colon D(A) \subset E \rightarrow E$ is a generator of a C 0 $C_{0}$ -semigroup, and F : [ 0 , T ] × E ⊸ E $F \colon [0,T] \times E \multiMap E$ is a nonlinear Multivalued Map. By using the method of the generalized translation Multivalued operator and a fixed point theorem for condensing Multivalued Maps, we prove the existence of a mild solution to this inclusion satisfying the nonlocal boundary value condition: x ( 0 ) ∈ Δ ( x ) , $$ x(0)\in \Delta (x), $$ where Δ : C ( [ 0 , T ] ; E ) ⊸ E $\Delta : C([0,T];E) \multiMap E$ is a given Multivalued Map. The semidiscretization scheme is developed and applied to the approximation of solutions to the considered nonlocal boundary value problem.
Nicole F. Sanderson - One of the best experts on this subject based on the ideXlab platform.
-
Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series
SIAM Journal on Applied Dynamical Systems, 2015Co-Authors: Zachary Alexander, Elizabeth Bradley, James D. Meiss, Nicole F. SandersonAbstract:Topology-based analysis of time-series data from dynamical systems is powerful: it potentially allows for computer-based proofs of the existence of various classes of regular and chaotic invariant sets for high-dimensional dynamics. Standard methods are based on a cubical discretization of the dynamics and use the time series to construct an outer approximation of the underlying dynamical system. The resulting Multivalued Map can be used to compute the Conley index of isolated invariant sets of cubes. In this paper we introduce a discretization that uses instead a simplicial complex constructed from a witness-landmark relationship. The goal is to obtain a natural discretization that is more tightly connected with the invariant density of the time series itself. The time-ordering of the data also directly leads to a Map on this simplicial complex that we call the witness Map. We obtain conditions under which this witness Map gives an outer approximation of the dynamics and thus can be used to compute the C...
-
Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series
arXiv: Chaotic Dynamics, 2014Co-Authors: Zachary Alexander, Elizabeth Bradley, James D. Meiss, Nicole F. SandersonAbstract:Topology based analysis of time-series data from dynamical systems is powerful: it potentially allows for computer-based proofs of the existence of various classes of regular and chaotic invariant sets for high-dimensional dynamics. Standard methods are based on a cubical discretization of the dynamics and use the time series to construct an outer approximation of the underlying dynamical system. The resulting Multivalued Map can be used to compute the Conley index of isolated invariant sets of cubes. In this paper we introduce a discretization that uses instead a simplicial complex constructed from a witness-landmark relationship. The goal is to obtain a natural discretization that is more tightly connected with the invariant density of the time series itself. The time-ordering of the data also directly leads to a Map on this simplicial complex that we call the witness Map. We obtain conditions under which this witness Map gives an outer approximation of the dynamics, and thus can be used to compute the Conley index of isolated invariant sets. The method is illustrated by a simple example using data from the classical H\'enon Map.
Tomasz Kaczynski - One of the best experts on this subject based on the ideXlab platform.
-
Linking Combinatorial and Classical Dynamics: Conley Index and Morse Decompositions
Foundations of Computational Mathematics, 2020Co-Authors: Bogdan Batko, Marian Mrozek, Tomasz Kaczynski, Thomas WannerAbstract:We prove that every combinatorial dynamical system in the sense of Forman, defined on a family of simplices of a simplicial complex, gives rise to a Multivalued dynamical system F on the geometric realization of the simplicial complex. Moreover, F may be chosen in such a way that the isolated invariant sets, Conley indices, Morse decompositions and Conley–Morse graphs of the combinatorial vector field give rise to isomorphic objects in the Multivalued Map case.
-
Multivalued Maps as a tool in modeling and rigorous numerics
Journal of Fixed Point Theory and Applications, 2008Co-Authors: Tomasz KaczynskiAbstract:Applications of the fixed point theory of Multivalued Maps can be classified into several areas: (1) Game theory and mathematical economics; (2) Discontinuous differential equations, differential inclusions, and optimal control; (3) Computing homology of Maps; (4) Computer assisted proofs in dynamics; (5) Digital imaging. We give an overview of the most classical and well developed areas of applications (1) and (2), where a Multivalued Map is used as a generalization of a single-valued continuous Map, and we survey more recent applications (3), (4), and (5), where Multivalued Maps play the role of a numerical tool.
Valeri Obukhovskii - One of the best experts on this subject based on the ideXlab platform.
-
Existence and approximation of solutions to nonlocal boundary value problems for fractional differential inclusions
Fixed Point Theory and Applications, 2019Co-Authors: Mikhail Kamenskii, Valeri Obukhovskii, Garik Petrosyan, Jen-chih YaoAbstract:We study a semilinear fractional order differential inclusion in a separable Banach space E of the form $$ {}^{C}D^{q}x(t)\in Ax(t)+ F\bigl(t,x(t)\bigr),\quad t\in [0,T], $$ where \({}^{C}D^{q}\) is the Caputo fractional derivative of order \(0 < q < 1\), \(A \colon D(A) \subset E \rightarrow E\) is a generator of a \(C_{0}\)-semigroup, and \(F \colon [0,T] \times E \multiMap E\) is a nonlinear Multivalued Map. By using the method of the generalized translation Multivalued operator and a fixed point theorem for condensing Multivalued Maps, we prove the existence of a mild solution to this inclusion satisfying the nonlocal boundary value condition: $$ x(0)\in \Delta (x), $$ where \(\Delta : C([0,T];E) \multiMap E\) is a given Multivalued Map. The semidiscretization scheme is developed and applied to the approximation of solutions to the considered nonlocal boundary value problem.
-
On connections between some selection and approximation results for Multivalued Maps
Topology and its Applications, 2008Co-Authors: Boris Gel'man, Valeri ObukhovskiiAbstract:Abstract We study the general conditions on a family of values of a Multivalued Map under which the existence of single-valued approximations may be derived from continuous selection results.
