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2005 | 25 | 1 | 5-18
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On the semilinear integro-differential nonlocal Cauchy problem

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EN
In this paper, we prove an existence theorem for the pseudo-non-local Cauchy problem $x'(t) + Ax(t) = f(t,x(t),∫_{t₀}^{t} k(t,s,x(s))ds)$, x₀(t₀) = x₀ - g(x), where A is the infinitesimal generator of a C₀ semigroup of operator ${T(t)}_{t > 0}$ on a Banach space. The functions f,g are weakly-weakly sequentially continuous and the integral is taken in the sense of Pettis.
Twórcy
  • Faculty of Mathematics and Computer Science, A. Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
  • Institute of Mathematics and Physics, University of Technology and Agriculture, Al. Prof. S. Kaliskiego 7, 85-796 Bydgoszcz
Bibliografia
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  • [17] A.R. Mitchell and Ch. Smith, An existence theorem for weak solutions of differential equations in Banach spaces, in: ''Nonlinear Equations in Abstract Spaces'', ed. V. Lakshmikantham, Academic Press (1978), 387-404.
  • [18] S.K. Ntouyas and P.Ch. Tsamatos, Global existence for semilinear evolution equations with non-local conditions, J. Math. Anal. Appl. 210 (1997), 679-687.
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  • [20] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Applied Mathematical Sciences, 44. Springer-Verlag, New York-Berlin 1983.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1055
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