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Degenerate nonlinear volterra integral equations in hilbert space

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Part of the Lecture Notes in Mathematics book series (LNM,volume 737)

Keywords

  • Hilbert Space
  • Maximal Monotone
  • Maximal Monotone Operator
  • Nonlinear Volterra Integral Equation
  • Sobolev Equation

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References

  1. BARBU, V.-Nonlinear Semigroups and Differential Equations in Banach Spaces, Noordhoff International Publishing & Ed.Academiei, Leyden-Bucharest 1976.

    CrossRef  MATH  Google Scholar 

  2. -Nonlinear Volterra Equations in a Hilbert Space, SIAM J. Math. Anal. Vol.6 (1975), p.728–741.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. -Existence for Nonlinear Volterra Equations in Hilbert Spaces, SIAM J.Math.Anal. Vol.9 (1978).

    Google Scholar 

  4. BARBU, V. and MALIK, M.A.-Semilinear Integro-differential equations in Hilbert Space, J.Math.Anal.Appl. (to appear)

    Google Scholar 

  5. BARDOS, C. BREZIS, H.-Sur une classe de problemes d'evolution non linéaire, J. Differential Equations 6(1969), 343–345.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. BRILL, S.-Sobolev Equations in Banach Space, J. Differential Equations 24(1977), 412–425.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. COLEMAN, B.D. GURTIN, M.E.-Equipresence and constitutive equations for rigid heat conductors, ZAMP 18(1967), 199–208.

    CrossRef  MathSciNet  Google Scholar 

  8. CRANDAL, M.G. LONDEN, S.O. NOHEL, J.A.-An abstract nonlinear Volterra integro-differential equation, J.Math.Anal.Appl. (to appear).

    Google Scholar 

  9. DUBINSKI, J.-Weak convergence in nonlinear elliptic and parabolic equations, Amer. Math.Soc.Transl. 67(1968), 226–258.

    CrossRef  Google Scholar 

  10. GURTIN, M.E. PIPKIN, A.C.-A general theory of heat condition with finite wave speeds, Arch.Rat. Mech.Anal. 31(1968), 113–126.

    CrossRef  MathSciNet  MATH  Google Scholar 

  11. GRANGE, O. MIGNOT, F.-Sur la résolution d'une équation et d'une inéquation paraboliques non linéaires, J. Functional Analysis 11(1972), 77–92.

    CrossRef  MathSciNet  MATH  Google Scholar 

  12. GRIPENBERG, G.-An existence result for a nonlinear Volterra integral equation in Hilbert space, Report HTKK-MAT-A 86, 1976.

    Google Scholar 

  13. LAGNESE, J.-General boundary value problems for differential equations of Sobolev type, SIAM J. Math.Anal. 3(1972), 105–119.

    CrossRef  MathSciNet  MATH  Google Scholar 

  14. LIONS, J.L.-Quelques méthodes de résolution des problèmes aux limites non linéaires, Dunod, Paris, 1969.

    MATH  Google Scholar 

  15. LONDEN, S.O.-On an integral equation in a Hilbert space, SIAM J.Math Anal.

    Google Scholar 

  16. LONDEN N, S.O. STAFFANS, O.J.-A note on Volterra integral equations in a Hilbert space,Report HTKK MAT-A 90(1976).

    Google Scholar 

  17. MACCAMY, R.C.-Stability theorems for a class of functional differential equations, SIAM J.Appl.Math.

    Google Scholar 

  18. -An integro-differential equation with application in heat flow, Quart.Appl. Math. 35(1977),1–19.

    MathSciNet  MATH  Google Scholar 

  19. MIGNOT, F.-Un théorème d'existence et d'unicité pour une équation parabolique non linéaire, Seminaire Brézis-Lions 1973/1974.

    Google Scholar 

  20. NUNZIATO, J.-On heat conduction in materials with memory, Quart.Appl.Math. 29(1971), 187–203.

    MathSciNet  MATH  Google Scholar 

  21. SHOWALTER, R.E.-Existence and representation theorems for a semilinear Sobolev equation in Banach space, SIAM J. Math.Anal. 3(1972), 527–543.

    CrossRef  MathSciNet  MATH  Google Scholar 

  22. -A nonlinear parabolic Sobolev equation, J. Math. Anal. Appl. 50(1975), 183–190.

    CrossRef  MathSciNet  MATH  Google Scholar 

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© 1979 Springer-Verlag

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Barbu, V. (1979). Degenerate nonlinear volterra integral equations in hilbert space. In: Londen, SO., Staffans, O.J. (eds) Volterra Equations. Lecture Notes in Mathematics, vol 737. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0064491

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  • DOI: https://doi.org/10.1007/BFb0064491

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09534-7

  • Online ISBN: 978-3-540-35035-4

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