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Tytuł artykułu

On some existence results of mild solutions for nonlocal integrodifferential Cauchy problems in Banach spaces

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Abstrakty
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In this paper, we study a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. Existence results of mild solutions are proved for a class of integrodifferential evolution equations with nonlocal initial conditions in Banach spaces. The main results are obtained by using the Schaefer fixed point theorem and semigroup theory. Finally, an example is given for demonstration.
Rocznik
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443--455
Opis fizyczny
Bibliogr. 16 poz.
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autor
Bibliografia
  • [1] 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.
  • [2] L. Byszewski, Existence, uniqueness and asymptotic stability of solutions of abstract nonlocal Cauchy problems, Dynam. Systems Appl. 5 (1996), 595–605.
  • [3] L. Byszewski, H. Akca, Existence of solutions of a semilinear functional differential evolution nonlocal problem, Nonlinear Anal. 34 (1998), 65–72.
  • [4] L. Byszewski, H. Akca, On a mild solution of a semilinear functional-differential evolution nonlocal problem, J. Appl. Math. Stochastic Anal. 10 (1997), 265–271.
  • [5] K. Balachandran, M. Chandrasekaran, The nonlocal Cauchy problem for semilinear integrodifferential equation with devating argument, Proceedings of the Edinburgh Mathematical Society 44 (2001), 63–70.
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  • [8] J.H. Liu, K. Ezzinbi, Non-autonomous integrodifferential equations with nonlocal conditions, Journal of Integral Equations and Applications 15 (2003), 79–93.
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  • [10] S.K. Ntouyas, P. Tsamatos, Global existence for semilinear evolution equations with nonlocal conditions, J. Math. Anal. Appl. 210 (1997), 679–687.
  • [11] H. Schaefer, Über die methode der priori Schranhen, Math. Ann 129 (1955), 415–416.
  • [12] JinRong Wang, W. Wei, A Class of Nonlocal Impulsive Problems for Integrodifferential Equations in Banach Spaces, Results. Math. 58 (2010), 379–397.
  • [13] JinRongWang, W.Wei, YanLong Yang, Fractional nonlocal integrodifferential equations of mixed type with time-varying generating operators and optimal control, Opuscula Math. 30 (2010), 217–234.
  • [14] JinRong Wang, YanLong Yang, W. Wei, Nonlocal impulsive problems for fractional differential equations with time-varying generating operators in Banach spaces, Opuscula Math. 30 (2010), 361–381.
  • [15] JinRong Wang, W. Wei, Y. Yang, Fractional nonlocal integrodifferential equations and its optimal control in Banach spaces, J. KSIAM 14 (2010), 79–91.
  • [16] X. Xue, Existence of solutions for semilinear nonlocal Cauchy problems in Banach spaces, Elec. J.D.E. 2005 (2005) 64, 1–7.
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Bibliografia
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bwmeta1.element.baztech-article-AGHT-0005-0071
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