On existence of mild and classical solutions of second order impulsive implicit differential equations

• Autorzy: Jain, R. S. , Reddy, B. S. , Kadam, S. D.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we establish the existence and uniqueness results of mild and classical solutions for impulsive implicit second order differential equations with nonlocal condition by using contraction principle. Furthermore, we give an example to illustrate our results.

Słowa kluczowe

EN

nonlocal condition; impulsive; differential equation

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 61
• Strony: 71--81
• Opis fizyczny: Bibliogr. 14 poz.

Twórcy

autor

Jain, R. S.

• School of Mathematical Sciences S. R. T. M. University Nanded-431 606, India,

autor

Reddy, B. S.

• School of Mathematical Sciences S. R. T. M. University Nanded-431 606,

autor

Kadam, S. D.

• School of Mathematical Sciences S. R. T. M. University Nanded-431 606, India,

Bibliografia

• [1] Anguraj A., Arjunan M.M., Existence and uniqueness of mild and classical solutions of impulsive evolution equations, Electronic Journal of Differential Equations, 111(1-8)(2005).
• [2] Bainov D., Simeonov P., Impusive Differential Equations, Periodic Solutions and Applications, John Wiley and Sons, Inc., New York (1993).
• [3] Bochenek J., An abstract nonlinear second order differential equation, Annales Polonici Mathematici Liv., 2(1991).
• [4] Byszewski L., An abstract nonlocal functional differential second order evolution problem, Technical Transactions, 1(2017), 147-154, D0I:10.4467/ 235373XCT.17.012.6109.
• [5] Hernandez M.E., A second order impulsive Cauchy problem, Cadernos de Mathematica, 2(2001), 299-238.
• [6] Jain R.S., Dhakne M.B., On impulsive nonlocal integro-differential equations with finite delay, International Journal of Mathematics Research, 5(4)(2013), 361-373.
• [7] Jain R.S., Dhakne M.B., On mild solutions of nonlocal semilinear impulsive functional integro-differential equations, Malaya Journel of Mathematik, 3(1)(2013), 27-33.
• [8] Jain R.S., Dhakne M.B., On mild solutions of nonlocal second order semilinear functional integro-differential equations, Fasciculi Mathemathici, 53(2014).
• [9] Lan H.-Y., Cvi Y.-S., Perturbation technique for a class of nonlinear implicit semilinear impulsive integro-differential equations of mixed type with noncompactness measure, Lan and Cul Advances in Difference Equations, 11(2015), DOI 10.1186/s13662-014-0329-y.
• [10] Lakshmikantham V., Bainov D.D., Simeonov P.S., Theory Of Impulsive Differential Equations, World Scientific Singapore, (1889).
• [11] Liu J.H., Nonlinear impulsive evolution equations, Dynam. Contin. Discrete Impuls. Systems, 6(1999), 77-85.
• [12] Muglia L., Pietramala P., Second order impulsive differential equations with functional intial conditions on unbounded intervals, Journal of Function Spaces and Applications, Vol. 2013, 9 pages, (2013), Article ID 479049.
• [13] Paul T., Anguraj A., Existence and uniqueness of nonliner impulsive integro-differential equations, Discrete Contin. Dyn. Syst. Ser. B., 6(2006), 1991-1198.
• [14] Samoilenko A.M., Perestyuk N.A., Impulsive Differential Equations, World Scientific, Singapore, (1995).

Uwagi

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

Identyfikatory

DOI

10.1515/fascmath-2018-0018