On a nonlinear dynamic integrodifferential equation on time scales

• Autorzy: Pachpatte D. B.
• Języki publikacji: EN

Abstrakty

EN

The main objective of the present paper is to study some basic qualitative properties of solutions of a certain nonlinear integrodifferential equation on time scales. The tools employed in the analysis are based on the applications of the Banach fixed point theorem and a certain inequality with explicit estimate on time scales.

Słowa kluczowe

EN

integrodifferential equation; time scales; qualitative properties; Banach fixed point theorem; inequalities with explicit estimates; existence and uniqueness; estimate on the solution; continuous dependence

PL

równanie różniczkowo-całkowe; skala czasu; właściwości jakościowe; twierdzenie Banacha o kontrakcji; nierówność; szacowanie rozwiązań; zależność ciągła

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2010
• Tom: Vol. 16, nr 2
• Strony: 279--294
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Pachpatte D. B.

• Department of Mathematics, Dr. B.A.M. University, Aurangabad, Maharashtra 431004, India,

Bibliografia

• [1] A. Bielecki, Une remarque sur la method de Banach-Caecipoli-Tikhonov dans la theorie des equations differentilies ordinaries, Bull. Acad. Polon. sci. Str. sci. Math. Phys. Astr., 4 (1956), 261-264.
• [2] M. Bohner and A. Peterson, Dynamic equations on Time Scales, Birkhauser Boston/Berlin, 2001.
• [3] M. Bohner and A. Peterson, Advances in Dynamic Equations on Time Scales, Birkhauser Boston/Berlin, 2003.
• [4] E. A. Bohner, M. Bohner and F. Akin, Pachpatte inequalities on time scales, J. Inequal. Pure. Appl. Math. 6(1) (2005), Art 6.
• [5] H. Brunner, Collection methods for Volterra integral and related functional differential equations, Cambridge University Press, Cambridge (2004).
• [6] C. Corduneanu, Integral equations and applications, Cambridge University Press, 1991.
• [7] C. Constantin, Topological Transversality: Application to an Integrodifferential Equation, J. Math. Anal. Appl., 197 (1996), 855-863.
• [8] S. Hilger, Analysis on measure chain - a unified approch to continuous and discrete calculus. Results Math. 18:18-56, 1990.
• [9] T. Kulik and C. C. Tisdell, Volterra integral equations on time scales: Basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Int. J. Difference. Eqn. 3 (2008), no. 1, 103-133.
• [10] B.G. Pachpatte, Applications of the Leray-Schauder alternative to some Volterra integral and integrodifferential equations, Indian J. Pure Appl. Math., 26 (1995), 1161-1168.
• [11] B.G. Pachpatte, Bounds on certain integral inequalities, J. Inequal. Pure and Appl. Math., 3 (3) (2002), Art 47.
• [12] B. G. Pachpatte, Inequalities for Finite Difference Equations, Marcel Dekker Inc., New York, 2002.
• [13] B. G. Pachpatte, Integral and Finite Difference Inequalities and Applications, North-Holland Mathematics Studies, Vol. 205, Elsevier Science B. V, Amesterdam, 2006.
• [14] B. G. Pachpatte, On certain Volterra integral and integrodifferential equations. Fact. Univ. (Nis) Sen Math. Infor, 23 (2008), 1-12.
• [15] D. B. Pachpatte, Explicit estimates on integral inequalities with time scale, J. In-equal. Pure and Appl. Math., 6 (1) (2005), Art 143.
• [16] C. C. Tisdell and A. Zaidi, Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling. Nonlinear Anal. 68 (2008), 3504-3524.
• [17] C. C.Tisdell and A. Zaidi, Successive approximations to solutions of dynamic equations on time scales. Comm. Appl. Nonlinear Anal. 16 (2009), no. 1, 61-87.