COMPOSITION FUNCTIONS MEASURABLE
Keywords:
Keywords: Integro-differential equation, Lyapunov functional, Nonlinear, Stability.Abstract
In this paper, the stability of a class of nonlinear integro-differential equation is investigated and analyzed. By defining a suitable Lyapunov functional we establish necessary and sufficient condition -for the stability of the zero solution. Our results extends known results in the literature.
References
de Amo, E., Diaz Carrillo, M., Fernandez-Sanchez, J.: Functionc with Unusual Differentiability Properties. Annals of the Alexandru Ioan Cuza University – Mathematics (2014)
cabada, A., Pouso, R.L.: Extremal solutions of strongly nonlinear discontinuous second-order equations with nonlinear functional boundary conditions. Nonlinear Analysis 42(8)., 1377-1396 (2000)
Folland, G>B.: Real analysis: modern techniques and their applications, 2 edn. PAM. Wiley (1999)
Monteiro, G.A., Slavik, A., Tvrdy, M.: Kurzweil- Stieltjes Integral: theory and applications. World Scientific, Singapore (2018)
Marquez Albes, I., Tojo, F.A.F.: Existence and Uniqueness of Solution for Stieltjes Differential Equations with Several Derivators. Mediterranean Journal of Mathematics 18(5), 181(2021)
Munroe, M.E.: Introduction to measure and integration. Addison-Wesley Cambridge, Mass. (1953)
Natanson, I.: Theory of functions of a real variable, Vol.I, rev.ed. 5 pr. Edn. Ungar (1983)
Saks, S.: Theory of the Integral, 2 edn. Dover Books on Advanced Mathematics. Dover, New York (1964)
Spataru, S.: An absolutely continuous function whose inverse function is not absolutely continuous. Note di Matematica 1 (2004).