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1
Content available Pseudo almost periodic solutions of infinite class under the light of measure theory
Votsia Djokata, Zabsonre Issa
Silesian Journal of Pure and Applied Mathematics
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2020
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vol. 10, iss. 1
15--43
EN
The aim of this work is to present new approach to study weighted pseudo almost periodic functions with infinite delay using the measure theory. We present a new concept of weighted ergodic functions which is more general than the classical one. Then we establish many interesting results on the functional space of such functions. We study the existence and uniqueness of (μ, ν)-pseudo almost periodic solutions of infinite class for some neutral partial functional differential equations in a Banach space when the delay is distributed on ]−∞, 0] using the spectra decomposition of the phase space developed in Adimy and co-authors.
2
Content available remote Second order evolution differential functional equations with infinite delay
Człapiński T., Karpowicz A.
Commentationes Mathematicae
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2018
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Vol. 58, No. 1/2
93--104
EN
We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
3
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.
4
Content available Global convergence of successive approximations of the Darboux problem for partial functional differential equations with infinite delay
Człapiński T.
Opuscula Mathematica
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2014
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Vol. 34, no. 2
327--338
EN
We consider the Darboux problem for the hyperbolic partial functional differential equation with infinite delay. We deal with generalized (in the "almost everywhere" sense) solutions of this problem. We prove a theorem on the global convergence of successive approximations to a unique solution of the Darboux problem.
5
Content available remote Existence and controllability results for mixed functional integrodifferential equations with infinite delay
Kucche K. D.
Demonstratio Mathematica
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2014
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Vol. 47, nr 4
893--909
EN
Sufficient conditions are established for the existence of solution for mixed neutral functional integrodifferential equations with infinite delay. The results are obtained using the theory of fractional powers of operators and the Sadovskii’s fixed point theorem. As an application we prove a controllability result for the system.
6
Content available remote On Exponential Stability of Volterra Difference Equations with Infinite Delay
Ngoc P. H. A., Hieu L. T.
Bulletin of the Polish Academy of Sciences. Mathematics
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2014
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Vol. 62, no 2
125--137
EN
General nonlinear Volterra difference equations with infinite delay are considered. A new explicit criterion for global exponential stability is given. Furthermore, we present a stability bound for equations subject to nonlinear perturbations. Two examples are given to illustrate the results obtained.
7
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.
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