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Abstract

Let Ω be a bounded domain of Rn.

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References

  • Amann H. (1976), Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces, SIAM Review, Vol.18, 620–709.

    Article  Google Scholar 

  • Bénilan P. et al. (1989), Recent advances in nonlinear elliptic and parabolic problems, Longman.

    Google Scholar 

  • Bertiger W. (1978), Maximum principles, gradient estimates, and weak solutions for second order partial differential equations, Trans. A.M. S., Vol.238, 213–227.

    Google Scholar 

  • Bertiger W. and Cosner C. (1979), Systems of second order equations with nonnegative characteristic form, Comm. in Partial Differential Equations, Vol.4, 701–737.

    Article  Google Scholar 

  • Clement P. and Sweers (1987), Getting a solution between sub-and supersolutions without monotone iteration, Rend. Istit. Mat. Univ. Triste, Vol.19, 189–194.

    Google Scholar 

  • Cosner C. and Schaefer (1987), On the development of functionals which satisfy a maximum principle, Applicable Analysis, Vol.26, 45–60.

    Article  Google Scholar 

  • Gilbarg D. and Trudinger N. S. (1983), Elliptic partial differential equations of second order, Springer-Verlag, Berlin.

    Book  Google Scholar 

  • Hong C.W. (1983), Necessary and sufficient conditions for a class of generalized maximum principle, Acta Math. Sinica, Vol.26, No. 3, 307–321.

    Google Scholar 

  • Kawohl B. (1983), On a maximum principles and Liouville theorems for quasi linear elliptic equations and systems, Comm. Math. Univ. Caroline, Vol.4, No.4, 647–655.

    Google Scholar 

  • Krylov N. V. (1987), Nonlinear elliptic and parabolic equations of the second order, Reidel Publ. Company, Boston.

    Book  Google Scholar 

  • Leung A.W. (1989), System of nonlinear partial differential equations, Kluwer Acad. Publ., Boston.

    Google Scholar 

  • Mandras F. (1976), Principio di massimo debale per sotoosoluzioni di sistemi lineari elliptici debalmente accoppiati, Ball. U.M.I., Vol. 13-A, 593–600.

    Google Scholar 

  • Maz’ya V. G. and Kresin G.I. (1984), The maximum principle for second-order strongly elliptic and parabolic with constant coefficients (Russian), Vol.125, No.4, 458–480.

    Google Scholar 

  • Peetre J. et Rus I. A. (1967), Sur la positivité de la fonction de Green, Math. Scand., Vol.21, 80–89.

    Google Scholar 

  • Protter M. H. (1982), The maximum principle and the eigenvalue problems, Proceed. of the 1980 Beijing Symposium on Differential Geometry and Diff.Eq., 787–860, Scienses Press, Beijing.

    Google Scholar 

  • Rus I. A. (1968), Sur les propriétés des normes des solutions d’un system d’équations différentielles du second ordre, Studia Univ. Babeş-Bolyai, fas. 1, 19–26.

    Google Scholar 

  • Rus I. A. (1969), Un principe du maximum pour les solutions d’un système fortement elliptique, Glasnik Matematicki, Vol.4, 75–77.

    Google Scholar 

  • Rus I.A. (1987), Some vector maximum principle for second order elliptic systems, Mathematica, Vol.29, 89–92.

    Google Scholar 

  • Rus I.A. (1988), Maximum principle for strongly elliptic systems: a conjecture, Babeş-Bolyai Univ. Preprint Nr.8, 43–46.

    Google Scholar 

  • Sabitov K. B. (1991), Maximum principles for some elliptic and hyperbolic systems of the second order (Russian), Vol.27, Nr.2, 272–278.

    Google Scholar 

  • Schaefer P. W. (editor: 1988), Maximum principles and eigenvalue problems in partial differential equations, Longman, New York.

    Google Scholar 

  • Schröder J. (1980), Operator inequalities, Acad. Press, New York.

    Google Scholar 

  • Tsai L.-Y. (1980), Existence of solutions of nonlinear elliptic systems, Bull.Inst. Math. Acad. Sinica, Vol.8, Nr.1, 111–127.

    Google Scholar 

  • Vidossich G. (1979), Comparison, existence, uniqueness and successive approximations for the Dirichlet problem of elliptic equations, Univ. of Texas at Arlington, Tech. Report No.119.

    Google Scholar 

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© 1992 Springer Basel AG

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Rus, I.A. (1992). Maximum Principles for Elliptic Systems. In: Barbu, V., Tiba, D., Bonnans, J.F. (eds) Optimization, Optimal Control and Partial Differential Equations. International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Série Internationale d’Analyse Numérique, vol 107. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8625-3_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8625-3_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9704-4

  • Online ISBN: 978-3-0348-8625-3

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