About DML-CZ | FAQ | Conditions of Use | Math Archives | Contact Us
  Previous |  Up |  Next

Article

Jianfu, Yang
Multiple solutions of semilinear elliptic systems. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 39 (1998), issue 2, pp. 257-268
MSC: 35J50, 35J55, 35J60, 47H15 | MR 1651942 | Zbl 0940.35072
Keywords:
indefinite; semilinear; elliptic system
Summary:
We obtain in this paper a multiplicity result for strongly indefinite semilinear elliptic systems in bounded domains as well as in $\Bbb R^N$.
References:
[A] Adams R.A.: Sobolev Spaces. Academic Press, 1975. MR 0450957 | Zbl 1098.46001
[BL] Berestycki H., Lions P.L.: Nonlinear scalar field equations, I and II. Arch. Rational Mech. Anal. 82 (1983), 313-376. MR 0695535
[CGM] 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. MR 0468913
[FF] de Figueiredo D.G., Felmer P.L.: On superquadratic elliptic systems. Trans. Amer. Math. Soc. 343 (1994), 99-116. MR 1214781 | Zbl 0799.35063
[FY] 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
[GT] Gilbarg D., Trudinger N.S.: Elliptic Partial Differential Equations of Second Order. Springer-Verlag, 1983. MR 0737190 | Zbl 1042.35002
[HE] Heinz H.P.: Existence and gap-bifurcation of multiple solutions to certain nonlinear eigenvalue problems. Nonlinear Anal. TMA 21 (1993), 457-484. MR 1240897 | Zbl 0793.47060
[HV] Hulshof J., van der Vorst R.: Differential systems with strongly indefinite variational structure. J. Funct. Anal. 114 (1993), 32-58. MR 1220982 | Zbl 0793.35038
[JW] Weidmann J.: Linear Operators in Hilbert Spaces. GMT 68, Springer-Verlag, 1980. MR 0566954 | Zbl 1025.47001
[KA] Kato T.: Perturbation Theory for Linear Operators. Springer-Verlag, 1966. MR 0203473 | Zbl 0836.47009
[LM] Lions J.L., Magenes E.: Non-homogeneous Boundary Value Problems and Applications, I. Springer-Verlag, 1972.
[PA] Palais R.: The principle of symmetric critically. Comment. Math. Phys. 69 (1979), 19-30. MR 0547524
[PL] Lions P.L.: Symétrie et compacité dans les espaces de Sobolev. J. Funct. Anal. 49 (1982), 315-334. MR 0683027 | Zbl 0501.46032
[R] 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
[S] Strauss W.: Existence of solitary waves in higher dimensions. Comment. Math. Phys. 55 (1977), 149-162. MR 0454365 | Zbl 0356.35028
Partner of
EuDML logo