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Keywords:
Schrödinger’s operators; weighted Sobolev spaces; maximum principle; min-max formula; noncooperative systems
Summary:
Using an approximation method, we show the existence of solutions for some noncooperative elliptic systems defined on an unbounded domain.
References:
[1] R. A. Adams: Sobolev spaces. Academic Press, New York-San Francisco-London, 1978. MR 0450957 | Zbl 0347.46040
[2] K. J.  Brown, C.  Cosner, and J. Fleckinger: Principal eigenvalues for problems with indefinite weight functions on $\mathbb{R}^{N}$. Proc. Amer. Math. Soc. 109 (1990), 147–155. MR 1007489
[3] L.  Boccardo, J.  Fleckinger-Pellé, and F.  de Thélin: Existence of solutions for some nonlinear cooperative systems. Differential Integral Equations 7 (1994), 689–698. MR 1270098
[4] L.  Cardoulis: Problèmes elliptiques: Applications de la théorie spectrale et étude de systèmes, existence de solutions. PhD Thesis, Univ. des Sc. Sociales de Toulouse, 1997.
[5] G.  Caristi, E.  Mitidieri: Maximum principles for a class of non-cooperative elliptic systems. Delft Progr. Rep. 14 (1990), 33–56. MR 1045316
[6] D. G.  Costa, C. A. Magalhães: A variational approach to noncooperative elliptic systems. Nonlinear Anal. 25 (1995), 699–715. MR 1341522
[7] A. Djellit: Valeurs propres de problèmes elliptiques indéfinis sur des ouverts non bornés de $\mathbb{R}^{N}$. PhD Thesis, U.P.S., Toulouse, 1992.
[8] A.  Djellit, J. Fleckinger: Valeurs propres de problèmes elliptiques. Boll. Unione Mat. Ital., VII.  Ser. B7 (1993), 857–874. MR 1255651
[9] A. Djellit, A.  Yechoui: Existence and non-existence of a principal eigenvalue for some boundary value problems. Maghreb Math. Rev. 6 (1997), 29–37. MR 1489164
[10] J.  Fleckinger-Pellé, J.  Hernández, F.  de Thélin: Principe du maximum pour un système elliptique non linéaire. C.R. Acad. Sci. Paris Sér. I Math. 314 (1992), 665–668.
[11] J. Fleckinger-Pellé, J.  Hernández, and F.  de Thélin: On maximum principle and existence of solutions for some cooperative elliptic systems. Differential Integral Equations 8 (1995), 69–85.
[12] J. Fleckinger, J.  Hernández, and F.  de Thélin: A maximum principle for linear cooperative elliptic systems. In: Differential Equations with Applications to Mathematical Physics, W. F. Ames, E. M. Harrell, and J. V. Herod (eds.), Acad. Press, Boston, 1993, pp. 79–86. MR 1207142
[13] D. G.  de Figueiredo, E.  Mitidieri: A maximum principle for an elliptic system and applications to a semilinear problem. SIAM J.  Math. Anal. 17 (1986), 836–849. MR 0846392
[14] D. G. de Figueiredo, E.  Mitidieri: Maximum principle for cooperative elliptic systems. C.R. Acad. Sci. Paris Sér. I Math. 310 (1990), 49–52. MR 1044413
[15] D. G. de Figueiredo, E.  Mitidieri: Maximum principle for linear elliptic systems. Quaterno Matematico 177, Dip. Sc. Mat, Univ. Trieste, 1988.
[16] J.  Fleckinger-Pellé, H.  Serag: Semilinear cooperative elliptic systems on  $\mathbb{R}^{N}$. Rend. Mat. Appl. (7) 15 (1995), 89–108. MR 1330181
[17] B. Hanouzet: Espaces de Sobolev avec poids, application au problème de Dirichlet dans un demi espace. Rend. Sem. Mat. Univ. Padova 46 (1971), 227–272. MR 0310417
[18] M. H.  Protter, H. F.  Weinberger: Maximum Principles in Differential Equations. Prentice Hall, Englewood Cliffs, 1967. MR 0219861
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