On mild solutions of nonlocal second order semilinear functional integro-differential equations

• Autorzy: Jain, R. S. , Dhakne, M. B.
• Języki publikacji: EN

Abstrakty

EN

In the present paper, we investigate the existence, uniqueness and continuous dependence on initial data of mild solutions of second order nonlocal semilinear functional integro-differential equations of more general type with delay in Banach spaces. Our analysis is based on the theory of strongly continuous cosine family of operators and modified version of Banach contraction theorem.

Słowa kluczowe

EN

existence; uniqueness; functional; integro-differential equation; fixed point; second order; cosine family

• Czasopismo: Fasciculi Mathematici
• Rocznik: 2014
• Tom: Nr 53
• Strony: 65--75
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Jain, R. S.

• School of Mathematical Sciences Swami Ramanand Teerth Marathw University Nanded-431606, India,

autor

Dhakne, M. B.

• Department of Mathematics Dr. Babasaheb Ambedkar Marathwada University Aurangabad-431004, India,

Bibliografia

• [1] BURTON T.A., Volterra Integral and Differential Eąuations, Academic Press, New York, 1983.
• [2] Byszewski L., On mild solution of a semilinear functional differential evolution nonlocal problem, J. of Appl. Maths. and Stoch. Anal., 10(3)(1997), 265-271.
• [3] Byszewski L., Akca H., Existence of solutions of a semilinear functional evolution nonlocal problem, Nonlinear Anal., 34(1998), 65-72.
• [4] Byszewski L., Lakshamikantham V., Theorem about the existence and uniqueness of a solution of a nonlocal abstract Cauchy problem in a Banach space, Applicable Anal., 40(1990), 11-19.
• [5] Corduneanu C., Integral Equations and Stability of Feedback System, Academic Press, New York, 1973.
• [6] Dugundji J., Granas A., Fixed Point Theory, Monografie Matematyczne PWN, Warszawa, 1982.
• [7] Fattorini H.O., Second order linear differential equations in Banach spaces, North Holland Mathematics Studies, 1985.
• [8] Fitzgibbon W.E., Global existence and boundedness of solutions of the extensible beam equation, SIAM J. Math. Anal., 13(1982), 739-745.
• [9] Hale J.K., Theory of Functional Differential Equations, Springer, 1977.
• [10] Lin Y., Liu J.H., Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Analysis: Theory, Meth. and Appl., 26(1996), 1023-1033.
• [11] Ntouyas S.K., Initial and boundary value problems for functional differential equations via the topological transversality method: A survey, Bull. Greek Math. Soc., 1998.
• [12] Ntouyas S.K., Nonlocal initial and boundary value problems: A survey, Handbook of differential equations: Ordinary differential equations, 2(2006), 461-557.
• [13] Pachpatte B.G., Inequalities for Differential and Integral Equations, Academic Press, 1998.
• [14] Pazy A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer Verlag, New York, 1983.
• [15] Siddiqi A.H., Functional Analysis with Applications, Tata McGraw-Hill Pub-lishing ltd, New Delhi, 1986.
• [16] Tidke H.L., Dhakne M.B., On abstract nonlinear differential equations of second order, Advances in Differential Equations and Control Processes, 3(1)(2009), 33-39.
• [17] Trayis C.C., Webb G.F., Second order Differential Equations in Banach Spaces, Proc. Int. Symp. On Non equations in abstract spaces, Academic Press, New York (1978), 331-361.
• [18] Trayis C.C., Webb G.F., Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Sci. Hungaricae, 32(1978), 76-96.
• [19] Trayis C.C., Webb G.F., An abstract second order semilinear Volterra integro differential equations, SIAM J. Math. Anal., 10(1979), 412-424.