Multiple solutions of semilinear elliptic systems
Jianfu, Yang
Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998), p. 257-268 / Harvested from Czech Digital Mathematics Library
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We obtain in this paper a multiplicity result for strongly indefinite semilinear elliptic systems in bounded domains as well as in $\Bbb R^N$.

Publié le : 1998-01-01
Classification:  35J50,  35J55,  35J60,  47H15 
@article{119004,
     author = {Yang Jianfu},
     title = {Multiple solutions of semilinear elliptic systems},
     journal = {Commentationes Mathematicae Universitatis Carolinae},
     volume = {39},
     year = {1998},
     pages = {257-268},
     zbl = {0940.35072},
     mrnumber = {1651942},
     language = {en},
     url = {http://dml.mathdoc.fr/item/119004}
}

Jianfu, Yang. Multiple solutions of semilinear elliptic systems. Commentationes Mathematicae Universitatis Carolinae, Tome 39 (1998) pp. 257-268. http://gdmltest.u-ga.fr/item/119004/

Adams R.A. Sobolev Spaces, Academic Press, 1975. | MR 0450957 | Zbl 1098.46001

Berestycki H.; Lions P.L. Nonlinear scalar field equations, I and II, Arch. Rational Mech. Anal. 82 (1983), 313-376. (1983) | MR 0695535

Coleman S.; Glazer V.; Martin A. Action minima among solutions to a class of Euclidean scalar field equations, Comment. Math. Phys. 58 (1978), 211-221. (1978) | MR 0468913

De Figueiredo D.G.; Felmer P.L. On superquadratic elliptic systems, Trans. Amer. Math. Soc. 343 (1994), 99-116. (1994) | MR 1214781 | Zbl 0799.35063

De Figueiredo D.G.; Yang Jianfu Decay, symmetry and existence of solutions of semilinear elliptic systems, to appear in Nonlinear Anal. TMA. | MR 1617988 | Zbl 0938.35054

Gilbarg D.; Trudinger N.S. Elliptic Partial Differential Equations of Second Order, Springer-Verlag, 1983. | MR 0737190 | Zbl 1042.35002

Heinz H.P. Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems, Nonlinear Anal. TMA 21 (1993), 457-484. (1993) | MR 1240897 | Zbl 0793.47060

Hulshof J.; Van Der Vorst R. Differential systems with strongly indefinite variational structure, J. Funct. Anal. 114 (1993), 32-58. (1993) | MR 1220982 | Zbl 0793.35038

Weidmann J. Linear Operators in Hilbert Spaces, GMT 68, Springer-Verlag, 1980. | MR 0566954 | Zbl 1025.47001

Kato T. Perturbation Theory for Linear Operators, Springer-Verlag, 1966. | MR 0203473 | Zbl 0836.47009

Lions J.L.; Magenes E. Non-homogeneous Boundary Value Problems and Applications, I, Springer-Verlag, 1972.

Palais R. The principle of symmetric critically, Comment. Math. Phys. 69 (1979), 19-30. (1979) | MR 0547524

Lions P.L. Symétrie et compacité dans les espaces de Sobolev, J. Funct. Anal. 49 (1982), 315-334. (1982) | MR 0683027 | Zbl 0501.46032

Rabinowitz P. Minimax methods in critical point theory with applications to differential equations, CBMS Regional Conf. Ser. in Math., No. 65, Amer. Math. Soc., Providence, R.I., 1986. | MR 0845785 | Zbl 0609.58002

Strauss W. Existence of solitary waves in higher dimensions, Comment. Math. Phys. 55 (1977), 149-162. (1977) | MR 0454365 | Zbl 0356.35028