Existence and asymptotic stability of continuous solutions for integral equations of product type
Article Sidebar
Main Article Content
Abstract
In this paper, we study the existence of a continuous solution for a nonlinear integral equation of a product type. The analysis uses the techniques of measures of noncompactness and Darbo's fixed point theorem. Our results are obtained under rather general assumptions. Moreover, the method used in the proof allows us to obtain the asymptotic stability of the solutions.
Downloads
Metrics
Article Details
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
- Authors keep the rights and guarantee the Journal of Innovative Applied Mathematics and Computational Sciences the right to be the first publication of the document, licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License that allows others to share the work with an acknowledgement of authorship and publication in the journal.
- Authors are allowed and encouraged to spread their work through electronic means using personal or institutional websites (institutional open archives, personal websites or professional and academic networks profiles) once the text has been published.
References
A. Abdeldaim, On some new Gronwall-Bellman-Ou-Iang type integral inequalities to study certain epidemic models, J. Integral Equations Appl. 24 (2012), 149–166.
A. Ardjouni and A. Djoudi, Approximating solutions of nonlinear hybrid Caputo fractional integro-differential equations via Dhage iteration principle, Ural Math. J. 5 (2019), 3–12.
N. T. J. Bailey, The mathematical theory of infectious diseases and its applications, Hafner, New York, 1975.
J. Banas and K. Goebel, Measures of noncompactness in Banach spaces, Lecture Notes in Pure and Applied Mathematics, Dekker, New York, 1980.
J. Banas and L. Olszowy, Measures of noncompactness related to monotonicity, Comment. Math. 41 (2001), 13–23.
J. Banas and J. Rivero, On measures of weak noncompactness, Ann. Mat. Pura Appl. 151 (1988), 213–224.
J. Banas and B. Rzepka, On existence and asymptotic stability of solutions of a nonlinear integral equation, J. Math. Anal. Appl. 284(1) (2003), 165–173.
A. Bellour, M. Bousselsal and M. A. Taoudi, Integrable solutions of a nonlinear integral equation related to some epidemic models, Glas. Mat. 49(2) (2014), 395–406.
B. Boulfoul, A. Bellour and S. Djebali, Solvability of nonlinear integral equations of product type, Electron. J. Differ. Equ. 19 (2018), 1–20.
O. Diekmann, A note on the asymptotic speed of propagation of an epidemic, J. Differ. Equations 33(1) (1979), 58–73.
G. Gripenberg, Periodic solutions of an epidemic model, J. Math. Biol. 10 (1980), 271–280.
G. Gripenberg, On some epidemic models, Quart. Appl. Math. 39(3) (1981), 317–327.
L. Li, F. Meng and P. Ju, Some new integral inequalities and their applications in studying the stability of nonlinear integro-differential equations with time delay, J. Math. Anal. Appl. 377 (2011), 853–862.
I. M. Olaru, Generalization of an integral equation related to some epidemic models, Carpathain J. Math. 26(1) (2010), 92–96.
B. G. Pachpatte, On a new inequality suggested by the study of certain epidemic models, J. Math. Anal. Appl. 195(1) (1995), 638–644.
P. Waltman, Deterministic threshold models in the theory of epidemics, Lecture Notes in Biomathematics, vol. 1, Springer-Verlag, New York, 1974.