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Pseudo almost periodic solutions of infinite class under the light of measure theory

Votsia Djokata, Zabsonre Issa

Silesian Journal of Pure and Applied Mathematics

2020

vol. 10, iss. 1

15--43

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.

Global existence and asymptotic behavior for a nonlinear degenerate SIS model

Ziane T. A.

Opuscula Mathematica

2013

Vol. 33, no. 4

615--630

In this paper we investigate the global existence and asymptotic behavior of a reaction diffusion system with degenerate diffusion arising in the modeling and the spatial spread of an epidemic disease.

Global solution of reaction diffusion system with non diagonal matrix

Moumeni A., Derradji L. S.

Demonstratio Mathematica

2012

Vol. 45, nr 1

81-93

The purpose of this paper is to prove the global existence in time of solutions for the coupled reaction-diffusion system: (…) with triangular matrix of diffusion coefficients. By combining the Lyapunov functional method with the regularizing effect, we show that global solutions exist. Our investigation applied for a wide class of the nonlinear terms f and g.