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1
Content available remote Existence and uniqueness of mild solutions for a fractional differential equation under Sturm-Liouville boundary conditions when the data function is of Lipschitzian type
Harjani Jackie, López Belen, Sadarangani Kishin
Demonstratio Mathematica
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2020
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Vol. 53, nr 1
167--173
EN
In this article, we present a sufficient condition about the length of the interval for the existence and uniqueness of mild solutions to a fractional boundary value problem with Sturm-Liouville boundary conditions when the data function is of Lipschitzian type. Moreover, we present an application of our result to the eigenvalues problem and its connection with a Lyapunov-type inequality.
2
Content available Weak solutions of fractional order differential equations via Volterra-Stieltjes integral operator
El-Sayed A. M. A., El-Sayed W. G., Abd El-Mowla A. A. H.
Journal of Mathematics and Applications
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2017
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Vol. 40
85--96
EN
The fractional derivative of the Riemann-Liouville and Caputo types played an important role in the development of the theory of fractional derivatives, integrals and for its applications in pure mathematics ([18], [21]). In this paper, we study the existence of weak solutions for fractional differential equations of Riemann-Liouville and Caputo types. We depend on converting of the mentioned equations to the form of functional integral equations of Volterra-Stieltjes type in reflexive Banach spaces.
3
Content available Existence and controllability results for Sobolev-type fractional impulsive stochastic differential equations with infinite delay
Boudaoui A., Slama A.
Journal of Mathematics and Applications
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2017
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Vol. 40
37--58
EN
In this paper, we prove the existence of mild solutions for Sobolev-type fractional impulsive stochastic di erential equations with in nite delay in Hilbert spaces. In addition, the controllability of the system with nonlocal conditions and in nite delay is studied. An example is provided to illustrate the obtained theory.
4
Content available remote Second order evolution equations with nonlocal conditions
Benchohra M., Nieto J. J., Rezoug N.
Demonstratio Mathematica
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2017
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Vol. 50, nr 1
309--319
EN
In this paper, we shall establish sufficient conditions for the existence of solutions for second order semilinear functional evolutions equation with nonlocal conditions in Fréchet spaces. Our approach is based on the concepts of Hausdorff measure, noncompactness and Tikhonoff’s fixed point theorem. We give an example for illustration.
5
Content available Fractional evolution equation nonlocal problems with noncompact semigroups
Zhang X, Chen P.
Opuscula Mathematica
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2016
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Vol. 36, no. 1
123--137
EN
This paper is concerned with the existence results of mild solutions to the nonlocal problem of fractional semilinear integro-differential evolution equations. New existence theorems are obtained by means of the fixed point theorem for condensing maps. The results extend and improve some related results in this direction.
6
Content available Measure of noncompactness and neutral functional differential equations with state-dependent delay
Benchohra M., Henderson J., Medjadj I.
Journal of Mathematics and Applications
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2016
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Vol. 39
23--45
EN
Our aim in this work is to study the existence of solutions of first and second order for neutral functional differential equations with state-dependent delay. We use the Mönch’s fixed point theorem for the existence of solutions and the concept of measures of noncompactness.
7
Content available Controllability of semilinear systems with fixed delay in control
Kumar S., Sukavanam N.
Opuscula Mathematica
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2015
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Vol. 35, no. 1
71--83
EN
In this paper, different sufficient conditions for exact controllability of semilinear systems with a single constant point delay in control are established in infinite dimensional space. The existence and uniqueness of mild solution is also proved under suitable assump­tions. In particular, local Lipschitz continuity of a nonlinear function is used. To illustrate the developed theory some examples are given.
8
Content available Existence and controllability results for damped second order impulsive functional differential systems with state-dependent delay
Arjunan M. M., Nadaf N. Y.
Opuscula Mathematica
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2014
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Vol. 34, no. 3
503--522
EN
In this paper, we investigate the existence and controllability of mild solutions for a damped second order impulsive functional differential equation with state-dependent delay in Banach spaces. The results are obtained by using Sadovskii’s fixed point theorem combined with the theories of a strongly continuous cosine family of bounded linear operators. Finally, an example is provided to illustrate the main results.
9
Content available remote Global Attractor for a Class of Parabolic Equations with Infinite Delay
Anh C. T., Hieu L. V., Thanh D. T. P.
Bulletin of the Polish Academy of Sciences. Mathematics
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2014
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Vol. 62, no 1
49--60
EN
We prove the existence of a compact connected global attractor for a class of abstract semilinear parabolic equations with infinite delay.
10
Content available remote On abstract nonlocal Cauchy problem
Bednarz A., Byszewski L.
Czasopismo Techniczne. Nauki Podstawowe
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2013
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R. 110, z. 1-NP
11--17
EN
In this paper, we investigate the existence and uniqueness of the classical solution to an abstract nonlocal Cauchy problem. For this purpose, we apply a notion of mild solution and the Banach contraction theorem.
PL
W artykule zbadano istnienie i jednoznaczność klasycznego rozwiązania abstrakcyjnego nielokalnego zagadnienia Cauchy’ego. W tym celu zastosowano rozwiązanie całkowe i twierdzenie Banacha o kontrakcji.
11
Content available remote Semilinear functional differential equations of fractional order with state-dependent delay
Benchohra M., Bennihi O., Ezzinbi K.
Commentationes Mathematicae
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2013
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Vol 53, No. 1
47--59
EN
In this paper we provide sufficient conditions for the existence and uniqueness of mild solutions for a class of semilinear functional differential equations of fractional order with state-dependent delay. The nonlinear alternative of Frigon- Granas type for contractions maps in Fr´echet spaces combined with -resolvent family is the main tool in our analysis.
12
Content available On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces
Yang Y., Wang J.
Opuscula Mathematica
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2011
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Vol. 31, no. 3
443-455
EN
In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.
13
Content available On an evolution inclusion in non-separable Banach spaces
Cernea A.
Opuscula Mathematica
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2009
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Vol. 29, no. 2
131-138
EN
We consider a Cauchy problem for a class of nonconvex evolution inclusions in non-separable Banach spaces under Filippov-type assumptions.We prove the existence of solutions.
14
Content available remote Nonlocal Cauchy problem in sun-reflexive space
Radoń M.
Czasopismo Techniczne. Nauki Podstawowe
|
2009
|
R. 106, z. 1-NP
55-61
EN
The aim of this paper is study the existence and uniqueness of mild and classical solution of the Cauchy problem for a linear and a semilinear evolution equation in Banach space with nonlocal condition. These theorems are proved by using the sun-reflexive Banach space relative to an operator A(0).
PL
Celem niniejszego artykułu jest zbadanie istnienia i jednoznaczności całkowego i klasycznego rozwiązania zagadnienia Cauchy'ego dla liniowego i semiliniowego równania ewolucyjnego w przestrzeni Banacha z nielokalnym warunkiem początkowym. Przedstawione w artykule twierdzenia zostały udowodnione przy założeniu sun-refleksywności przestrzeni Banacha względem operatora A(0).
15
Content available remote Semilinear Cauchy problems with almost sectorial operators
Dlotko T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2007
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Vol. 55, no 4
333-346
EN
Existence of a mild solution to a semilinear Cauchy problem with an almost sectorial operator is studied. Under additional regularity assumptions on the nonlinearity and initial data we also prove the existence of a classical solution to this problem. An example of a parabolic problem in Holder spaces illustrates the abstract result.
16
Content available remote On the existence of global solutions of evolution equations
Medved M.
Demonstratio Mathematica
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2004
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Vol. 37, nr 4
871--882
EN
In this paper a sufficient condition for the existence of global solutions of evolution equations is proved. In the proof a modification of the Bihari type integral inequality to the case of a weakly singular nonlinear integral inequality is used. An application to a reaction-diffusion problem is given.
17
Content available remote On some perturbations of some abstract differential equations
Diagana T., Nguerekata G. M.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
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2003
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[Z] 43(2)
201-206
EN
We are concerned with the existence of almost automorphic mild solutions to the perturbed abstract differential equations of the form x(t) = (A + B)x(t) (*), where A is a unbounded linear operator generator of a Co-group of bounded operators and B is a bounded linear operator acting in a Banach space X. Under suitable conditions we show that every bounded mild solution to (*) is almost automorphic. Meanwhile under a relatively compactness hypothesis of the range of a solution, we show that such a solution is also almost periodic.
18
Existence and controllability results for nonlinear differential inclusions with nonlocal conditions in Banach spaces
Benchohra M., Ntouyas S. K.
Journal of Applied Analysis
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2002
|
Vol. 8, nr 1
33-48
EN
In this paper we investigate the existence and controllability of mild solutions to the first order semilinear evolution inclusions in Banach spaces with nonlocal conditions. We shall rely of a fixed point theorem for condensing maps due to Martelli.
19
Content available remote Existence results on semiinfinite intervals for functional-differential and intergrodifferential inclusions in Banach spaces with nonlocal conditions
Benchohra M., Ntouyas S.
Demonstratio Mathematica
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2001
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Vol. 34, nr 4
795-807
20
Content available remote Existence of mild solutions on semi-infinite interval to second order differential equations with nonlocal conditions
Benchohra M., Ntouyas S.K.
Annales Societatis Mathematicae Polonae. Seria 1: Commentationes Mathematicae
|
2001
|
[Z] 41
41-49
EN
In this paper we investigate the existence of mild solutions, on a semi infinite interval, to the second order differential equations in Banach spaces with nonlocal conditions. We shall rely on the theorem of Schauder-Tychonoff.
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