On a nonlinear integrodifferential evolution inclusion with nonlocal initial conditions in Banach spaces

• Autorzy: Yan Z.
• Języki publikacji: EN

Abstrakty

EN

In this paper, we discuss the existence results for a class of nonlinear integrodifferential evolution inclusions with nonlocal initial conditions in Banach spaces. Our results are based on a fixed point theorem for condensing maps due to Martelli and the resolvent operators combined with approximation techniques.

Słowa kluczowe

EN

nonlinear integrodifferential evolution inclusions; fixed point; resolvent operator; nonlocal initial condition

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 2
• Strony: 377--394
• Opis fizyczny: Bibliogr. 31 poz.

Twórcy

autor

Yan Z.

• Hexi University Department of Mathematics Zhangye, Gansu 734000, P.R. China,

Bibliografia

• [1] S. Aizicovici, H. Lee, Nonlinear nonlocal Cauchy problems in Banach spaces, Appl.Math. Lett. 18 (2005), 401–407.
• [2] K. Balachandran, J.Y. Park, M. Chandrasekaran, Nonlocal Cauchy problems for delay integrodifferential equations of Sobolev type in Banach spaces, Appl. Math. Lett. 15 (2002), 845–854.
• [3] K. Balachandran, J.P. Dauer, Controllability of nonlinear systems in Banach spaces:A survey, J. Optim. Theory Appl. 115 (2002), 7–28.
• [4] J. Banas, K. Goebel, Measures of Noncompactness in Banach Spaces, Dekker, New York, 1980.
• [5] M. Benchohra, S.K. Ntouyas, Nonlocal Cauchy problems for neutral functional differential and integrodifferential inclusions in Banach spaces, J. Math. Anal. Appl. 258 (2001), 573–590.
• [6] M. Benchohra, S.K. Ntouyas, Controllability for functional differential and integrodifferential inclusions in Banach spaces, J. Optim. Theory Appl. 113 (2002), 449–472.
• [7] M. Benchohra, E.P. Gatsori, S.K. Ntouyas, Controllability results for semilinear evolution inclusions with nonlocal conditions, J. Optim. Theory Appl. 118 (2003), 493–513.
• [8] L. Byszewski, V. Lakshmikantham, Theorem about existence and uniqueness of a solutions of a nonlocal Cauchy problem in a Banach space, Appl. Anal. 40 (1990), 11–19.
• [9] L. Byszewski, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991), 494–505.
• [10] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional-differential evolution nonlocal problem, Nonlinear Anal. 34 (1998), 65–72.
• [11] K. Deimling, Multivalued Differential Equations, De Gruyter, Berlin, 1992.
• [12] K. Deng, Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. Math. Anal. Appl. 179 (1993), 630–637.
• [13] X. Fu, Controllability of neutral functional differential systems in abstract space, Appl. Math. Comput. 141 (2003), 281–296.
• [14] S. Hu, N. Papageorgiou, Handbook of Multivalued Analysis, Kluwer Academic Publishers,Dordrecht, Boston, 1997.
• [15] R. Grimmer, Resolvent operators for integral equations in Banach space, Trans. Amer.Math. Soc. 48 (1982), 333–349.
• [16] R. Grimmer, J.H. Liu, Integrated semigroups and integrodifferential equations, Semigroup Forum 48 (1994), 79–95.
• [17] M. Guo, X. Xue, R. Li, Controllability of impulsive evolution inclusions with nonlocal conditions, J. Optim. Theory Appl. 120 (2004), 355–374.
• [18] R.R. Kumar, Nonlocal Cauchy problem for analytic resolvent integrodifferential equations in Banach spaces, Appl. Math. Comput. 204 (2008), 352–362.
• [19] G. Li, X. Xue, Controllability of evolution inclusions with nonlocal conditions, Appl. Math. Comput. 141, (2003), 375–384.
• [20] A. Lasota, Z. Opial, An application of the Kakutani CKy Fan theorem in the theory of ordinary differential equations, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys.13 (1965), 781–786.
• [21] J. Liang, T.J. Xiao, Semilinear integrodifferential equations with nonlocal initial conditions, Comput. Math. Appl. 47 (2004), 863–875.
• [22] Y. Lin, J.H. Liu, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal. 26 (1996), 1023–1033.
• [23] J.H. Liu, Resolvent operators and weak solutions of integrodifferential equations, Differ. Integral Equ. 7 (1994), 523–534.
• [24] M. Martelli, A Rothe’s type theorem for noncompact acyclic-valued map, Boll. Un. Mat. Ital. 11 (1975) 3, 70–76.
• [25] S.K. Ntouyas, P.Ch. Tsamotas, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679–687.
• [26] S.K. Ntouyas, P.Ch. Tsamotas, Global existence for semilinear integrodifferential equations with delay and nonlocal conditions, Anal. Appl. 64 (1997), 99–105.
• [27] J. Pruss, On resolvent operators for linear integrodifferential equations of Volterra type, J. Integral Equations 5 (1983), 211–236.394 Zuomao Yan
• [28] M.D. Quinn, N. Carmichael, An approach to nonlinear control problem using fixed point methods, degree theory and pseudo-inverses, Numer. Funct. Anal. Optim. 23 (1991), 109–154.
• [29] Z. Yan, Nonlinear functional integrodifferential evolution equations with nonlocal conditions in Banach spaces, Math. Commun. 14 (2009), 35–45.
• [30] Z. Yan, Z. Pu, On solution of a nonlinear functional integrodifferential equations with nonlocal conditions in Banach space, Result. Math. 55 (2009), 493–505.
• [31] K. Yosida, Functional Analysis, 6th ed., Springer, Berlin, 1980.