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Solution set properties for some nonlinear parabolic differential equations

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Part of the Lecture Notes in Mathematics book series (LNM,volume 703)

Keywords

  • Minimal Solution
  • Lower Solution
  • Initial Boundary Value Problem
  • Parabolic Partial Differential Equation
  • Elliptic Differential Equation

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References

  1. K. Ako, On the Dirichlet problem for quasi-linear elliptic differential equations of second order, J. Math. Soc. Japan 13 (1961), 45–62.

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. H. Amann, On the existence of positive solutions of nonlinear elliptic boundary value problems, Ind. Univ. Math. J. 21 (1971), 125–146.

    CrossRef  MathSciNet  MATH  Google Scholar 

  3. J.W. Bebernes and K. Schmitt, Invariant sets and the Hukuhara-Kneser property for systems of parabolic partial differential equations, Rocky Mountain J. Math. 7 (1977), to appear.

    Google Scholar 

  4. J.W. Bebernes and K. Schmitt, On the existence of maximal and minimal solutions for parabolic partial differential equations, submitted.

    Google Scholar 

  5. K. Chueh, C. Conley, and J.A. Smoller, Positively invariant regions for systems of nonlinear diffusion equations, Indiana Math. J. 26 (1977), 373–392.

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. H.B. Keller, Elliptic boundary value problems suggested by nonlinear diffusion processes, Arch. Rat. Mech. Anal. 5 (1969), 363–381.

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. Krasnosel'skii, M., and Sobolevskii, Structure of the set of solutions of an equation of parabolic type, Ukranian. Math. J. 16 (1964), 319–333.

    CrossRef  MathSciNet  Google Scholar 

  8. M. Nagumo, On principally linear elliptic differential equations of second order, Osaka, Math. J. 6 (1954), 207–229.

    MathSciNet  MATH  Google Scholar 

  9. C.V. Pao, Positive solutions of a nonlinear boundary value problem of parabolic type, J. Diff. Eqs. 22 (1976), 145–163.

    CrossRef  MathSciNet  MATH  Google Scholar 

  10. J.P. Peul, Existence comportement al'infini et stabilite dans certaines problemes quasilineares elliptiques et paraboliques d'ordre 2, Ann. Scuola Norm. Sup. Pisa, Sec. IV 3 (197), 89–119.

    Google Scholar 

  11. R. Redheffer and W. Walter, Invariant sets for systems of partial differential equations, Arch. Rat. Mech. Anal., to appear.

    Google Scholar 

  12. D.H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Ind. J. Math. 211 (1972), 979–1000.

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Weinberger, H., Invariant sets for weakly coupled parabolic and elliptic systems, Rend. Math. 8 (1975), 295–310.

    MathSciNet  MATH  Google Scholar 

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© 1979 Spring-Verlag

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Bebernes, J.W. (1979). Solution set properties for some nonlinear parabolic differential equations. In: Fábera, J. (eds) Equadiff IV. Lecture Notes in Mathematics, vol 703. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0067252

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  • DOI: https://doi.org/10.1007/BFb0067252

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09116-5

  • Online ISBN: 978-3-540-35519-9

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