The Experts below are selected from a list of 279003 Experts worldwide ranked by ideXlab platform
Rahmat Ali Khan - One of the best experts on this subject based on the ideXlab platform.
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applicability of topological Degree Theory to evolution equation with proportional delay
Fractals, 2020Co-Authors: Muhammad Sher, Kamal Shah, Yuming Chu, Rahmat Ali KhanAbstract:In this paper, we use the topological Degree Theory (TDT) to investigate the existence and uniqueness of solution for a class of evolution fractional order differential equations (FODEs) with propo...
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qualitative analysis of multi terms fractional order delay differential equations via the topological Degree Theory
Mathematics, 2020Co-Authors: Muhammad Sher, Kamal Shah, Michal Feckan, Rahmat Ali KhanAbstract:With the help of the topological Degree Theory in this manuscript, we develop qualitative Theory for a class of multi-terms fractional order differential equations (FODEs) with proportional delay using the Caputo derivative. In the same line, we will also study various forms of Ulam stability results. To clarify our theocratical analysis, we provide three different pertinent examples.
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existence and uniqueness results to a coupled system of fractional order boundary value problems by topological Degree Theory
Numerical Functional Analysis and Optimization, 2016Co-Authors: Kamal Shah, Rahmat Ali KhanAbstract:ABSTRACTIn this article, we study existence and uniqueness results for a coupled system of nonlinear fractional order differential subject to nonlinear more general four-point boundary condition of the following type where 0 < α, β ≤ 1 and f, g ∈ C([0, 1] × ℝ2, ℝ) are continuous and the nonlocal functions ϕ, ψ: (I, ℝ) → ℝ are also continuous. The parameters η, ξ satisfy 0 < η < 1, 0 < ξ < 1, and λi, γi, μi(i = 1, 2) are real numbers. Some new existence and uniqueness results are developed for the coupled system using topological Degree Theory and some standard fixed point theorems. An example is also provided to illustrate our main result.
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Degree Theory and existence of positive solutions to coupled systems of multi point boundary value problems
Boundary Value Problems, 2016Co-Authors: Kamal Shah, Amjad Ali, Rahmat Ali KhanAbstract:In this article, we investigate existence and uniqueness of positive solutions to coupled systems of multi-point boundary value problems for fractional order differential equations of the form $$ \left \{ \textstyle\begin{array}{l} D^{\alpha} x(t)=\phi(t,x(t),y(t)), \quad t\in I=[0,1], \\ D^{\beta} y(t)=\psi(t,x(t),y(t)),\quad t\in I=[0,1], \\ x(0)=g(x),\qquad x(1)=\delta x(\eta),\quad 0< \eta< 1, \\ y(0)=h(y),\qquad y(1)=\gamma y(\xi),\quad 0< \xi< 1, \end{array}\displaystyle \right . $$ where $\alpha, \beta\in(1,2]$ , D denotes the Caputo fractional derivative, $0<\delta, \gamma<1$ are parameters such that $\delta\eta^{\alpha}<1$ , $\gamma\xi^{\beta}<1$ , $h, g\in C(I,\mathbb{R})$ are boundary functions and $\phi,\psi:I\times\mathbb{R} \times \mathbb{R} \rightarrow\mathbb{R}$ are continuous. We use the technique of topological Degree Theory to obtain sufficient conditions for existence and uniqueness of positive solutions to the system. Finally, we provide an example to illustrate our main results.
Athanassios G. Kartsatos - One of the best experts on this subject based on the ideXlab platform.
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the leray schauder approach to the Degree Theory for s perturbations of maximal monotone operators in separable reflexive banach spaces
Nonlinear Analysis-theory Methods & Applications, 2009Co-Authors: Boubakari Ibrahimou, Athanassios G. KartsatosAbstract:Abstract The purpose of this paper is to demonstrate the fact that the topological Degree Theory of Leray and Schauder may be used for the development of the topological Degree Theory for bounded demicontinuous ( S + ) -perturbations f of strongly quasibounded maximal monotone operators T in separable reflexive Banach spaces. Certain basic homotopy properties and the extension of this Degree Theory to (possibly unbounded) strongly quasibounded perturbations f are shown to hold. This work uses the well known embedding of Browder and Ton, and extends the work of Berkovits who developed this Theory for the case T = 0 . Besides being an interesting mathematical problem, the existence of such a Degree Theory may, conceivably, become useful in situations where the use of the Leray–Schauder Degree (via infinite dimensional compactness) is necessary.
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strongly quasibounded maximal monotone perturbations for the berkovits mustonen topological Degree Theory
Journal of Mathematical Analysis and Applications, 2008Co-Authors: Dhruba R Adhikari, Athanassios G. KartsatosAbstract:Abstract Let X be a real reflexive Banach space with dual X ∗ . Let L : X ⊃ D ( L ) → X ∗ be densely defined, linear and maximal monotone. Let T : X ⊃ D ( T ) → 2 X ∗ , with 0 ∈ D ( T ) and 0 ∈ T ( 0 ) , be strongly quasibounded and maximal monotone, and C : X ⊃ D ( C ) → X ∗ bounded, demicontinuous and of type ( S + ) w.r.t. D ( L ) . A new topological Degree Theory has been developed for the sum L + T + C . This Degree Theory is an extension of the Berkovits–Mustonen Theory (for T = 0 ) and an improvement of the work of Addou and Mermri (for T : X → 2 X ∗ bounded). Unbounded maximal monotone operators with 0 ∈ D ˚ ( T ) are strongly quasibounded and may be used with the new Degree Theory.
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a new topological Degree Theory for densely defined s l perturbations of multivalued maximal monotone operators in reflexive separable banach spaces
Nonlinear Analysis-theory Methods & Applications, 2008Co-Authors: Athanassios G. Kartsatos, Joseph QuarcooAbstract:Abstract Let X be a real reflexive separable locally uniformly convex Banach space with locally uniformly convex dual space X ∗ . Let T : X ⊃ D ( T ) → 2 X ∗ be maximal monotone, with 0 ∈ D ∘ ( T ) and 0 ∈ T ( 0 ) , and C : X ⊃ D ( C ) → X ∗ . Assume that L ⊂ D ( C ) is a dense linear subspace of X , C is of class ( S + ) L , and 〈 C x , x 〉 ≥ − ψ ( ‖ x ‖ ) , x ∈ D ( C ) , where ψ : R + → R + is nondecreasing. A new topological Degree Theory is developed for the sum T + C . The current approach utilizes the “approximate” Degree d ( T t + C , G , 0 ) , t ↓ 0 , ( T t ≔ ( T − 1 + t J − 1 ) − 1 , G ⊂ X open and bounded) of Kartsatos and Skrypnik for the single-valued mapping T t + C . The subdifferential ∂ φ , for φ belonging to a large class of proper convex lower semicontinuous functions, gives rise to operators T to which this Degree Theory applies. A theoretical application to an existence problem of nonlinear analysis is included.
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a new topological Degree Theory for densely defined quasibounded s perturbations of multivalued maximal monotone operators in reflexive banach spaces
Abstract and Applied Analysis, 2005Co-Authors: Athanassios G. Kartsatos, I V SkrypnikAbstract:Let X be an infinite-dimensional real reflexive Banach space with dual space X ∗ and G ⊂ X open and bounded. Assume that X and X ∗ are locally uniformly convex. Let T : X ⊃ D ( T ) → 2 X ∗ be maximal monotone and C : X ⊃ D ( C ) → X ∗ quasibounded and of type ( S ˜ + ) . Assume that L ⊂ D ( C ) , where L is a dense subspace of X , and 0 ∈ T ( 0 ) . A new topological Degree Theory is introduced for the sum T + C . Browder's Degree Theory has thus been extended to densely defined perturbations of maximal monotone operators while results of Browder and Hess have been extended to various classes of single-valued densely defined generalized pseudomonotone perturbations C . Although the main results are of theoretical nature, possible applications of the new Degree Theory are given for several other theoretical problems in nonlinear functional analysis.
Ruixi Liang - One of the best experts on this subject based on the ideXlab platform.
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Existence and uniqueness of periodic solution for forced Rayleigh type equations
Journal of Applied Mathematics and Computing, 2012Co-Authors: Ruixi LiangAbstract:By using the coincidence Degree Theory and some analysis skill, some new sufficient conditions for the existence and uniqueness of periodic solution for a kind of forced Rayleigh type equation are established, which are complement of previously known results.
Yongkun Li - One of the best experts on this subject based on the ideXlab platform.
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stability and existence of periodic solutions to delayed cohen grossberg bam neural networks with impulses on time scales
Neurocomputing, 2009Co-Authors: Yongkun Li, Xuerong Chen, Lu ZhaoAbstract:In this paper, by using the continuation theorem of coincidence Degree Theory and constructing some suitable Lyapunov functions, we study the stability and existence of periodic solutions to delayed Cohen-Grossberg BAM neural networks with impulses on time scales.
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existence and stability of periodic solutions for cohen grossberg neural networks with multiple delays
Chaos Solitons & Fractals, 2004Co-Authors: Yongkun LiAbstract:Abstract We use the continuation theorem of coincidence Degree Theory and Liapunov functions to study the existence and stability of periodic solutions for the Cohen–Grossberg neural network with multiple delays.
Teffera M Asfaw - One of the best experts on this subject based on the ideXlab platform.
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a Degree Theory for compact perturbations of monotone type operators and application to nonlinear parabolic problem
Abstract and Applied Analysis, 2017Co-Authors: Teffera M AsfawAbstract:Let be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space . Let be maximal monotone, be bounded and of type and be compact with such that lies in (i.e., there exist and such that for all ). A new topological Degree Theory is developed for operators of the type . The Theory is essential because no Degree Theory and/or existence result is available to address solvability of operator inclusions involving operators of the type , where is not defined everywhere. Consequently, new existence theorems are provided. The existence theorem due to Asfaw and Kartsatos is improved. The Theory is applied to prove existence of weak solution (s) for a nonlinear parabolic problem in appropriate Sobolev spaces.
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a new topological Degree Theory for pseudomonotone perturbations of the sum of two maximal monotone operators and applications
Journal of Mathematical Analysis and Applications, 2016Co-Authors: Teffera M AsfawAbstract:Abstract Let X be a real reflexive locally uniformly convex Banach space with locally uniformly convex dual space X ⁎ and G be a nonempty, bounded and open subset of X. Let T : X ⊇ D ( T ) → 2 X ⁎ and A : X ⊇ D ( A ) → 2 X ⁎ be maximal monotone operators. Assume, further, that, for each y ∈ X , there exists a real number β ( y ) and there exists a strictly increasing function ϕ : [ 0 , ∞ ) → [ 0 , ∞ ) with ϕ ( 0 ) = 0 , ϕ ( t ) → ∞ as t → ∞ satisfying 〈 w ⁎ , x − y 〉 ≥ − ϕ ( ‖ x ‖ ) ‖ x ‖ − β ( y ) for all x ∈ D ( A ) , w ⁎ ∈ A x , and S : X → 2 X ⁎ is bounded of type ( S + ) or bounded pseudomonotone such that 0 ∉ ( T + A + S ) ( D ( T ) ∩ D ( A ) ∩ ∂ G ) or 0 ∉ ( T + A + S ) ( D ( T ) ∩ D ( A ) ∩ ∂ G ) ‾ , respectively. New Degree Theory is developed for operators of the type T + A + S with Degree mapping d ( T + A + S , G , 0 ) . The Degree is shown to be unique invariant under suitable homotopies. The Theory developed herein generalizes the Asfaw and Kartsatos Degree Theory for operators of the type T + S . New results on surjectivity and solvability of variational inequality problems are obtained. The mapping theorems extend the corresponding results for operators of type T + S . The Degree Theory developed herein is used to show existence of weak solution of nonlinear parabolic problem in appropriate Sobolev spaces.
