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Weighted Sobolev spaces and the nonlinear Dirichlet problem in unbounded domains. (English) Zbl 0422.35038


MSC:

35J65 Nonlinear boundary value problems for linear elliptic equations
47H05 Monotone operators and generalizations
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
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[2] Benci, V.; Fortunato, D., Some compact embedding theorems for weighted Sobolev spaces, Boll. U.M.I., 13-B, 832-843 (1976) · Zbl 0382.46018
[3] Benci, V.; Fortunato, D., Discreteness conditions of the spectrum of Schrödinger operators, J. Math. Analysis and Appl., 64, 695-700 (1978) · Zbl 0389.35016 · doi:10.1016/0022-247X(78)90013-6
[4] Berger, M. S.; Schechter, M., Embedding theorems and quasilinear elliptic boundary value problems for unbounded domains, Trans. of the A.M.S., 172, 261-278 (1972) · Zbl 0253.35038 · doi:10.2307/1996347
[5] Brezis, H., Equations et inequations non lineaires dans les espaces vectoriels en dualiét, Ann. Inst. Fourier, Grenoble, 18, 115-175 (1968) · Zbl 0169.18602
[6] D. E. Edmund - W. D. Evans,Elliptic and degenerate elliptic operators in unbounded domains, Ann. Scuola Norm. Sup. di Pisa, III,27, pp. 592-640. · Zbl 0298.35027
[7] Edmund, D. E.; Webb, J. R. L., Quasi linear elliptic problems in unbounded domains, Proc. R. Soc. Lond., A 334, 397-410 (1975) · Zbl 0263.35034
[8] Hanouzet, B., Espace de Soblev avec poids; applications au problem de Dirichlet dans un demi espace, Rend. Sem. Mat. Univ. Padova, 56, 227-272 (1971) · Zbl 0247.35041
[9] P. Hess,Nonlinear elliptic problems in unbounded domains, to appear in « Abhandlungen der Akademie der Wissenschaften der DDR ». · Zbl 0367.35021
[10] Lions, J. L., Quelques methodes de resolution des problems aux limites non linearies (1969), Gauthier-Villars: Dunod, Gauthier-Villars · Zbl 0189.40603
[11] C. Parenti,Operatori pseudo-differenziali in R^n ed applicazioni, Ann. Mat. pura ed appl., (1972), pp. 359-389. · Zbl 0291.35070
[12] M. M. Vainberg,Variational methods for the study of non linear operators, Holden-Day, Inc. (1964). · Zbl 0122.35501
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