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Second order evolution differential functional equations with infinite delay

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a second order semilinear functional evolution equation with infinite delay in a Banach space. We prove the existence of mild solutions for this equation using the measure of noncompactness technique and the Schauder fixed point theorem.
Rocznik
Strony
93--104
Opis fizyczny
Bibliogr. 25 poz.
Twórcy
  • Institute of Mathematics, University of Gdańsk, Wit Stwosz St. 57, 80-309 Gdańsk, Poland
autor
  • Institute of Mathematics, University of Gdańsk, Wit Stwosz St. 57, 80-309 Gdańsk, Poland
Bibliografia
  • [1] A. Ambrosetti, Un teorema di esistenza per le equazioni differenziali negli spazi di Banach, Rend. Sem. Univ. Padova 39 (1967), 349-361.
  • [2] K. Balachandran, D. G. Park, and S. Marshal Anthoni, Existence of solutions of abstract nonlinear second-order neutral functional integrodifferential equations, Comput. Math. Appl. 46 (2003), 1313-1324, DOI 10.1016/s0898-1221( 03)90221-5.
  • [3] J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Lecture Notes in Pure App. Math., vol. 60, Marcel Dekker, New York 1980.
  • [4] M. Benchohra and N. Rezzoug, Measure of noncompactness and second order evolution equations, Gulf J. Math. 4 (2016), 71-79.
  • [5] G. A. Bocharov and F. A. Rihan, Numerical modelling in biosciences using delay differential equations, J. Comp. Appl. Math. 125 (2000), 183-199, DOI 10.1016/s0377-0427(00)00468-4.
  • [6] J. Bochenek, An abstract nonlinear second order differential equation, Ann. Pol. Math. 54 (1991), 155-166, DOI 10.4064/ap-54-2-155-166.
  • [7] J. Bochenek, Existence of the fundamental solution of a second order evolution equation, Ann. Pol. Math. 66 (1997), 15-35, DOI 10.4064/ap-66-1-15-35.
  • [8] T. Ergenç, B. Karasozen, and S. Piskarev, Approximation of semilinear Cauchy problem for the second order equation in Banach spaces, Nonlinear Anal. 28 (1997), 1157-1165, DOI 10.1016/s0362-546x(97)82866-0.
  • [9] J. K. Hale and J. Kato, Phase space for retarded equations with infinite delay, Funkcial. Ekvac. 21 (1978), 11-41.
  • [10] H. R. Henriquez, Existence of solutions of non-autonomous second order functional differential equations with infinite delay, Nonlinear Anal. 74 (2011), 3333-3352, DOI 10.1016/j.na.2011.02.010.
  • [11] H. R. Henriquez and J. C. Pozo, Existence of solutions of abstract non-autonomous second order integro-differential equations, Bound. Value Probl. 168 (2016), 24 pp., DOI 10.1186/s13661-016-0675-7.
  • [12] H. R. Henriquez and C. H. Vásquez, Difierentiability of solutions of the second order abstract Cauchy problem, Semigroup Forum 64 (2002), 472-488, DOI 10.1007/s002330010092.
  • [13] H. R. Henriquez and C. H. Vásquez, Differentiability of solutions of second-order functional differential equations with unbounded delay, J. Math. Anal. Appl. 280 (2003), 284-312, DOI 10.1016/s0022-247x(03)00042-8.
  • [14] E. Hernandez, K. Balachandran, and N. Annapoorani, Existence results for a damped second order abstract functional differential equation with impulses, Math. Comput. Modelling 50 (2009), 1583-1594, DOI 10.1016/j.mcm.2009.09.007.
  • [15] Y. Hino, S. Murakami, and T. Naito, Functional differential equations with infinite delay, Springer-Verlag, Berlin-Heidelberg-New York 1991, DOI 10.1007/bfb0084432, Lect. Notes Math.
  • [16] F. Kappel and W. Schappacher, Some considerations to fundamental theory of infinite delay equations, J. Differential Equations 37 (1980), 141-183, DOI 10.1016/0022-0396(80)90093-5.
  • [17] M. Kozak, A fundamental solution of a second-order differential equation in a Banach space, Univ. Iagel. Acta Math. 32 (1995), 275-289.
  • [18] V. Lakshmikantham, L. Wen, and B. Zhang, Theory of Differential Equations with Unbounded Delay, Kluwer, Dordrecht 1994, DOI 10.1007/978-1-4615-2606-3.
  • [19] W. Rzymowski, On the existence of solution of the equation x' = f (t, x) in a Banach space, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 16 (1968), 795-800.
  • [20] H. Serizawa and M. Watanabe, Time-dependent perturbation for cosine families in Banach spaces, Houston J. Math. 12 (1986), 579-586.
  • [21] J. S. Shin, An existence theorem of functional differential equations with infinite delay in a Banach space, Funkcial. Ekvac. 30 (1987), 19-29.
  • [22] H. L. Tidke and M. B. Dhakne, Existence and uniqueness of mild solutions of second order Volterra integro-differential equations with nonlocal conditions, Apll. Math. E-Note 9 (2009), 101-108.
  • [23] H. L. Tidke and M. B. Dhakne, Existence and uniqueness of solutions of certain second order nonlinear equations, Note Mat. 30 (2010), 73-81.
  • [24] C. C. Travis and G. F. Webb, Cosine families and abstract nonlinear second order differential equations, Acta Math. Acad. Scient. Hung. 32 (1978), 75-96, DOI 10.1007/bf01902205.
  • [25] J. Wu, Theory and Applications of Partial Functional Differential Equations, Springer Verlag, New York 1996, DOI 10.1007/978-1-4612-4050-1.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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