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Existence and Regularity for Semilinear Neutral Differential Equations in Hilbert Spaces

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In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

Abstract

In this paper, we construct some results on the existence and regularity for solutions of neutral functional differential equations with unbounded principal operators in Hilbert spaces. In order to establish the existence and regularity for solutions of the neutral system by using fractional power of operators and the local Lipschtiz continuity of nonlinear term without using many of the strong restrictions considering in the previous literature.

참고문헌 (6)

  1. E. Hernandez, "Existence results for partial neutral functional di erential equations with state-dependent delay", Math. Comput. Modell, 49, pp.1260~1267 (2009)
  2. J.P.C, "Existence results for a partial neutral integro-di erential equation with state-dependent delay", Elec. J. Qualitative Theory Di er. Equ, 29, pp.1~12 (2010)
  3. L. Wang, "Approximate controllability for integrodi erential equations and multiple delays", J. Optim. Theory Appl, 143, pp.185~206 (2009)
  4. H. Triebel, "Interpolation Theory, Function Spaces, Di erential Operators" (1978), North-Holland
  5. H. Tanabe, "Equations of Evolution" (1979), Pitman-London
  6. J. P. Aubin, "Un theoreme de compacite", C. R. Acad. Sci, 256, pp.5042~5044 (1963)

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