A nonstandard Volterra integral equation on time scales

• Autorzy: Reinfelds Andrejs , Christian Shraddha

Identyfikatory

DOI

10.1515/dema-2019-0042

• Języki publikacji: EN

Abstrakty

EN

This paper introduces the more general result on existence, uniqueness and boundedness for solutions of nonstandard Volterra type integral equation on an arbitrary time scales. We use Lipschitz type function and the Banach’s fixed point theorem at functional space endowed with a suitable Bielecki type norm. Furthermore, it allows to get new sufficient conditions for boundedness and continuous dependence of solutions.

Słowa kluczowe

EN

Volterra integral equations; time scales; bounded solution; continuous dependence

PL

równania całkowe Volterry; skala czasu; rozwiązania ograniczone; zależność ciągła

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 503--510
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Reinfelds Andrejs

• Institute of Mathematics and Computer Science, University of Latvia, 29 Raiņa bulvāris, Rīga, LV-1459
• Department of Mathematics, University of Latvia, 3 Jelgavas iela, LV-1004, Rīga, Latvia

autor

Christian Shraddha

• Department of Mathematics, University of Latvia, 3 Jelgavas iela, LV-1004, Rīga, Latvia

Bibliografia

• [1] Hilger S., Analysis on measure chains. A unified approach to continuous and discrete calculus, Results Math., 1990, 18, 18-56
• [2] Kulik T., Tisdeil C.C., Volterra integral equations on time scales. Basic qualitative and quantitative results with applications to initial value problems on unbounded domains, Int. J. Difference Equ., 2008, 3, 103-133
• [3] Pachpatte D.B., On a nonstandard Volterra type dynamic integral equation on time scales, Electron. J. Qual. Theory Differ. Equ., 2009, 72, 1-14
• [4] Pachpatte D.B., Properties of some dynamic integral equation on time scales, Ann. Funct. Anal., 2013, 4(2), 12-26
• [5] Reinfelds A., Christian S., Volterra integral equations on unbounded time scales, Int. J. Difference Equ., 2019, 14, 169-177
• [6] dos Santos I.L.D., On Volterra integral equations on time scales, Mediterr. J. Math., 2015, 12(2), 471-480
• [7] Ferguson B.S., Lim G.C., Dynamic Economic Models in Discrete Time. Theory and Empirical Applications, Routledge, London, 2003
• [8] Tisdeil C.C., Zaidi A., Basic qualitative and quantitative results for solutions to nonlinear dynamic equations on time scales with an application to economic modelling, Nonlinear Analysis, 2008, 68, 3504-3524
• [9] Bohner M., Peterson A., Dynamic Equations on Time Scales. An Introduction with Applications, Birkhäuser,Boston/Basel/Berlin, 2001
• [10] Bohner M., Peterson A., Advances in Dynamic Equations on Time Scales, Birkhäuser, Boston/Basel/Berlin, 2003
• [11] Bohner M., Some oscillation criteria for first order delay dynamic equations, Far East Journal of Applied Mathematics, 2005, 18, 289-304

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).