Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families-Reference-Cited by-同舟云学术

Mild solutions for some nonautonomous evolution equations with state-dependent delay governed by equicontinuous evolution families

Published:2023-10-01 Issue:S Volume:11 Page:227-240
ISSN:2321-5666
Container-title:Malaya Journal of Matematik
language:
Short-container-title:Malaya J. Mat.

Author:

Kpoumié Moussa El-Khalil,Djeunankam Yannick-Levis^ORCID,Mbang Joseph,Noundjeu Pierre

Abstract

In this work, we study the existence solutions and the dependence continuous with the initial data for some nondensely nonautonomous partial functional differential equations with state-dependent delay in Banach spaces. We assume that the linear part is not necessarily densely defined, satisfies the well-known hyperbolic conditions and generate a noncompact evolution family. Our existence results are based on Sadovskii fixed point Theorem. An application is provided to a reaction-diffusion equation with state-dependent delay.

Publisher

MKD Publishing House

Subject

General Medicine

Reference29 articles.

1. A KRID , T., M ANIAR , L., O UHINOU , A. , Periodic solutions of non densely nonautonomous differential

2. equations with delay, Afr. Diaspora J. Math., 15(1)(2013), 1–18.

3. A RENDT , W., G RABOSCH , A., G REINER , G., G ROH , U., L OTZ , H.P., M OUSTAKAS , U., N AGEL , R., N EUBRANDER , B., S CHLOTTERBECK , U. , One-parameter Semigroup of Positive Operators, Springer, Berlin (1984).

4. A RINO , O., H BIB , M.L.,A IT D ADS , E., Delay Differential Equations and Applications, Mathematics, Physics and Chemistry, 205(2002).

5. B ANA ’ S , J. , On measures of non compactness in Banach spaces, Comment. Math. Univ. Carolin., 21(1)(1980), 131–143.