Existence Results of Noncompact Impulsive Delay Evolution Inclusions

Pengxian ZHU

Abstract


This paper deals with a class of abstract Cauchy problems for impulsive delay evolution inclusions in the Banach spaces. By using measures of noncompactness, multi-valued analysis and fixed point theory, we establish the existence of mild solutions for the mentioned inclusions under the assumption that the semigroup generated by linear part is noncompact. Finally, an illustrating example is given.


Keywords


Impulsive evolution inclusions; Delay; Weakly upper semi-continuous; Measures of noncompactness

References


Ahmed, N. U. (2006). Measure solutions for impulsive evolution equations with measurable vector fields. J. Math. Anal. Appl., 319, 74-93.

Benchohra, M., Gatsori, E. P., Henderson, J., & Ntouyas, S. K. (2003). Nondensely defined evolution impulsive differential inclusions with nonlocal conditions. J. Math. Anal. Appl., 286, 307-325.

Benchohra, M., Henderson, J., & Ntouyas, S. K. (2006). Impulsive differential equations and inclusions (Vol.2). New York: Hindawi Publishing Corporation.

Bothe, D. (1998). Multi-valued perturbations of m-accretive differential inclusions. Israel J. Math., 108, 109-138.

Cardinali, T., & Rubbioni, P. (2008). Impulsive semilinear differential inclusions: Topological structure of the solution set and solutions on non-compact domains. Nonlinear Anal., 69(1), 73-84.

Chen, D. H., Wang, R. N., & Zhou, Y. (2013). Nonlinear evolution inclusions: Topological characteriza- tions of solution sets and applications. J. Funct. Anal., 265, 2039-2073.

Chuong, N. M., & Ke, T. D. (2012). Generalized Cauchy problems involving nonlocal and impulsive conditions. J. Evol. Equ., 12, 367-392.

Djebali, S., Gorniewicz, L., & Ouahab, A. (2011). Topological structure of solution sets for impulsive differential inclusions in Fréchet spaces. Nonlinear Anal., 74, 2141-2169.

Fec ̆kan, M., Zhou, Y., & Wang, J. R. (2012). On the concept and existence of solution for impulsive fractional differential equations. Commun. Nonlinear Sci. Numer. Simul., 17, 3050-3060.

Gabor, G., & Grudzka, A. (2012). Structure of the solution set to impulsive functional differential inclusions on the half-line. Nonlinear Differ. Equ. Appl., 19, 609-627.

Henry, D. (1981). Geometric theory of semilinear parabolic equations. Springer, Berlin.

Kamenskii, M., Obukhovskii, V., & Zecca, P. ( 2001). Condensing multi-valued maps and semilinear differential inclusions in banach spaces, de gruyter series in nonlinear analysis and applications (Vol.7). Walter de Gruyter, Berlin, New York.

Lakshmikantham, V., Bainov, D. D., & Simeonov, P. S. (1989). Theory of impulsive differential equations. Singapore: World Scientific Pub Co Inc.

O’Regan, D., & Precup, R. (2001). Existence criteria for integral equations in Banach spaces. J. Inequal. Appl., 6, 77-97.

Obukhovskii, V., & Yao, J. C. (2010). On impulsive functional differential inclusions with Hille-Yosida operators in Banach spaces. Nonlinear Anal., 73, 1715-1728.

Samoilenko, A. M., & Perestyuk, N. A. (1995). Impulsive differential equations, world scientific. Singapore.

Vrabie, I. I. (2012). Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditions. J. Funct. Anal., 262, 1363-1391.

Wang, R. N., & Zhu, P. X. (2013). Non-autonomous evolution inclusions with nonlocal history conditions: Global integral solutions. Nonlinear Anal., 85, 180-191.

Wang, R. N., & Ma, Q. H. (2015). Some new results for multi-valued fractional evolution equations. Appl. Math. Comput, 257, 285-294.




DOI: http://dx.doi.org/10.3968/n

Refbacks

  • There are currently no refbacks.


Copyright (c) 2017 Pengxian ZHU

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Share us to:   

Reminder

  • How to do online submission to another Journal?
  • If you have already registered in Journal A, then how can you submit another article to Journal B? It takes two steps to make it happen:

1. Register yourself in Journal B as an Author

  • Find the journal you want to submit to in CATEGORIES, click on “VIEW JOURNAL”, “Online Submissions”, “GO TO LOGIN” and “Edit My Profile”. Check “Author” on the “Edit Profile” page, then “Save”.

2. Submission

  • Go to “User Home”, and click on “Author” under the name of Journal B. You may start a New Submission by clicking on “CLICK HERE”.


We only use three mailboxes as follows to deal with issues about paper acceptance, payment and submission of electronic versions of our journals to databases:
caooc@hotmail.com; mse@cscanada.net; mse@cscanada.org

 Articles published in Management Science and Engineering are licensed under Creative Commons Attribution 4.0 (CC-BY).

 MANAGEMENT SCIENCE AND ENGINEERING Editorial Office

Address:1055 Rue Lucien-L'Allier, Unit #772, Montreal, QC H3G 3C4, Canada.

Telephone: 1-514-558 6138
Http://www.cscanada.net Http://www.cscanada.org

Copyright © 2010 Canadian Research & Development Centre of Sciences and Cultures