zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Stationary states of the nonlinear Dirac equation: A variational approach. (English) Zbl 0843.35114
Using variational techniques, the authors prove the existence of stationary solutions of some nonlinear Dirac equations.
35Q55NLS-like (nonlinear Schrödinger) equations
81Q05Closed and approximate solutions to quantum-mechanical equations
35A05General existence and uniqueness theorems (PDE) (MSC2000)
[1]Ambrosetti, A., Rabinowitz, P.H.: Dual variational methods in critical points theory and applications. J. Funct. Anal.14, 38–349 (1973) · Zbl 0273.49063 · doi:10.1016/0022-1236(73)90051-7
[2]Berestycki, H., Lions, P.-L.: Nonlinear scalar field equations. Arch. Rat. Mech. Anal.82, 313–346 (1983)
[3]Benci, V., Capozzi, A., Fortunato, D.: Periodic solutions of Hamiltonian systems with superquadratic potential. Ann. Mat. Pura et app. (IV), Vol.CXLIII, 1–46 (1986)
[4]Bjorken, J.D., Drell, S.D.: Relativistic quantum fields. New York: McGraw-Hill, 1965
[5]Balabane, M., Cazenave, T., Douady, A., Merle, F.: Existence of excited states for a nonlinear Dirac field. Commun. Math. Phys.119, 153–176 (1988) · Zbl 0696.35158 · doi:10.1007/BF01218265
[6]Balabane, M., Cazenave, T., Vazquez, L.: Existence of standing waves for Dirac fields with singular nonlinearities. Commun. Math. Phys.133, 53–74 (1990) · Zbl 0721.35065 · doi:10.1007/BF02096554
[7]Benci, V., Rabinowitz, P.H.: Critical point theorems for indefinite functionals, Inv. Math.52, 336–352 (1979) · Zbl 0465.49006 · doi:10.1007/BF01389883
[8]Cazenave, T.: On the existence of stationary states for classical non-linear Dirac fields. In: Hyperbolic systems and Mathematical Physics. Textos e Notas4, CMAF, Lisbonne, 1989
[9]Cazenave, T., Vazquez, L.: Existence of localized solutions for a classical nonlinear Dirac field. Commun. Math. Phys.105, 35–47 (1986) · Zbl 0596.35117 · doi:10.1007/BF01212340
[10]Finkelstein, R., Lelevier, R., Ruderman, M.: Phys. Rev.83, 326–332 (1951) · Zbl 0043.21603 · doi:10.1103/PhysRev.83.326
[11]Hofer, H., Wysocki, K.: First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann.288, 483–503 (1990) · Zbl 0702.34039 · doi:10.1007/BF01444543
[12]Lions, P.-L.: The concentration-compactness method in the Calculus of Variations. The locally compact case. Part. I: Anal. non-linéaire, Ann. IHP1, 109–145 (1984); Part. II: Anal. non-linéaire, Ann. IHP1, 223–283 (1984)
[13]Merle, F.: Existence of stationary states for nonlinear Dirac equations. J. Diff. Eq.74 (1), 50–68 (1988) · Zbl 0696.35154 · doi:10.1016/0022-0396(88)90018-6
[14]Rañada, A.F.: Classical nonlinear Dirac field models of extended particles. In: Quantum theory, groups, fields and particles (editor A.O. Barut). Amsterdam, Reidel: 1982
[15]Séré, E.: Homoclinic orbits on compact hypersurfaces in IR2N , of restricted contact type. Preprint CEREMADE 9238 (1992)
[16]Smale, S.: An infinite dimensional version of Sard’s theorem. Amer. J. Math.87, 861–866 (1965) · Zbl 0143.35301 · doi:10.2307/2373250
[17]Soler, M.: Phys. Rev.D1, 2766–2769 (1970)
[18]Strauss, W.A.: Existence of solitary waves in higher dimensions. Commun. Math. Phys.55, 149–162 (1977) · Zbl 0356.35028 · doi:10.1007/BF01626517
[19]Tanaka, K.: Homoclinic orbits in the first order superquadratic Hamiltonian system: convergence of subharmonics. J. Diff. Eq.94, 315–339 (1991) · Zbl 0787.34041 · doi:10.1016/0022-0396(91)90095-Q