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)
Soliton solutions for quasilinear Schrödinger equations. II. (English) Zbl 1229.35268
Summary: For a class of quasilinear Schrödinger equations, we establish the existence of ground states of soliton-type solutions by a variational method. For Part I see [{\it J. Liu} and {\it Z. Wang}, Proc. Am. Math. Soc. 131, No. 2, 441--448 (2003; Zbl 1229.35269)].

35Q55NLS-like (nonlinear Schrödinger) equations
35Q51Soliton-like equations
Full Text: DOI
[1] Ambrosetti, A.; Rabinowitz, P.: Dual variational methods in critical point theory. J. funct. Anal. 14, 349-381 (1973) · Zbl 0273.49063
[2] Arcoya, D.; Boccardo, L.: Critical points for multiple integrals of the calculus of variations. Arch. rational mech. Anal. 134, 249-274 (1996) · Zbl 0884.58023
[3] Arcoya, D.; Boccardo, L.: Some remarks on critical point theory for nondifferentiable functionals. Nonlinear differential equations appl. 6, 79-100 (1999) · Zbl 0923.35049
[4] Bartsch, T.; Wang, Z. -Q.: Existence and multiplicity results for some superlinear elliptic problems on rn. Comm. partial differential equations 20, 1725-1741 (1995) · Zbl 0837.35043
[5] Bass, F. G.; Nasanov, N. N.: Nonlinear electromagnetic spin waves. Phys. rep. 189, 165-223 (1990)
[6] Berestycki, H.; Lions, P. L.: Nonlinear scalar field equations, iexistence of a ground state. Arch. rational mech. Anal. 82, 313-346 (1983) · Zbl 0533.35029
[7] Borovskii, A. V.; Galkin, A. L.: Dynamical modulation of an ultrashort high-intensity laser pulse in matter. Jetp 77, 562-573 (1993)
[8] De Bouard, A.; Hayashi, N.; Saut, J. -C.: Global existence of small solutions to a relativistic nonlinear Schrödinger equation. Comm. math. Phys. 189, 73-105 (1997) · Zbl 0948.81025
[9] Brandi, H. S.; Manus, C.; Mainfray, G.; Lehner, T.; Bonnaud, G.: Relativistic and ponderomotive self-focusing of a laser beam in a radially inhomogeneous plasma. Phys. fluids B 5, 3539-3550 (1993)
[10] Browder, F. E.: Variational methods for nonlinear elliptic eigenvalue problems. Bull. amer. Math. soc. 71, 176-183 (1965) · Zbl 0135.15802
[11] Canino, A.: Multiplicity of solutions for quasilinear elliptic equations. Topol. methods nonlinear anal. 6, 357-370 (1995) · Zbl 0863.35038
[12] Chen, X. L.; Sudan, R. N.: Necessary and sufficient conditions for self-focusing of short ultraintense laser pulse. Phys. rev. Lett. 70, 2082-2085 (1993)
[13] Corvellec, J.; Degiovanni, M.; Marzocchi, M.: Deformation properties for continuous functionals and critical point theory. Topol. methods nonlinear anal. 1, 151-171 (1993) · Zbl 0789.58021
[14] Floer, A.; Weinstein, A.: Nonspreading wave packets for the cubic Schrödinger equation with a bounded potential. J. funct. Anal. 69, 397-408 (1986) · Zbl 0613.35076
[15] Hasse, R. W.: A general method for the solution of nonlinear soliton and kink Schrödinger equations. Z. phys. B 37, 83-87 (1980)
[16] Kondrat’ev, V.; Shubin, M.: Discreteness of spectrum for the Schrödinger operator on manifolds of bounded geometry. Operator theory: adv. Appl. 110, 185-226 (1999) · Zbl 0985.58012
[17] Kosevich, A. M.; Ivanov, B. A.; Kovalev, A. S.: Magnetic solitons. Phys. rep. 194, 117-238 (1990)
[18] Kurihura, S.: Large-amplitude quasi-solitons in superfluid films. J. phys. Soc. jpn 50, 3262-3267 (1981)
[19] Laedke, E. W.; Spatschek, K. H.; Stenflo, L.: Evolution theorem for a class of perturbed envelope soliton solutions. J. math. Phys. 24, 2764-2769 (1983) · Zbl 0548.35101
[20] Lange, H.; Toomire, B.; Zweifel, P. F.: Time-dependent dissipation in nonlinear Schrödinger systems. J. math. Phys. 36, 1274-1283 (1995) · Zbl 0823.35159
[21] Litvak, A. G.; Sergeev, A. M.: One dimensional collapse of plasma waves. JETP lett. 27, 517-520 (1978)
[22] Liu, J. -Q.; Wang, Z. -Q.: Soliton solutions for quasilinear Schrödinger equations. Proc. amer. Math. soc. 131, 441-448 (2003) · Zbl 1229.35269
[23] Makhankov, V. G.; Fedyanin, V. K.: Non-linear effects in quasi-one-dimensional models of condensed matter theory. Phys. rep. 104, 1-86 (1984)
[24] Nakamura, A.: Damping and modification of exciton solitary waves. J. phys. Soc. jpn 42, 1824-1835 (1977)
[25] Poppenberg, M.; Schmitt, K.; Wang, Z. Q.: On the existence of soliton solutions to quasilinear Schrödinger equations. Calc. var. Partial differential equations 14, 329-344 (2002) · Zbl 1052.35060
[26] Porkolab, M.; Goldman, M. V.: Upper hybrid solitons and oscillating two-stream instabilities. Phys. fluids 19, 872-881 (1976)
[27] Quispel, G. R. W.; Capel, H. W.: Equation of motion for the Heisenberg spin chain. Physica A 110, 41-80 (1982)
[28] P. Rabinowitz, Minimax methods in critical point theory with applications to differential equations, CBMS Conference Series in Mathematics, Vol. 65, American Mathematical Society, 1986. · Zbl 0609.58002
[29] Rao, M. M.; Ren, Z. D.: Theory of Orlicz spaces. (1991) · Zbl 0724.46032
[30] Ritchie, B.: Relativistic self-focusing and channel formation in laser-plasma interactions. Phys. rev. E 50, 687-689 (1994)
[31] Strauss, W. A.: Existence of solitary waves in higher dimensions. Comm. math. Phys. 55, 149-162 (1977) · Zbl 0356.35028
[32] Takeno, S.; Homma, S.: Classical planar Heisenberg ferromagnet, complex scalar fields and nonlinear excitations. Progr. theoret. Phys. 65, 172-189 (1981)
[33] Lions, P. -L.: Concentration compactness principle in the calculus of variations. The limit case. Part 1. Rev. mat. Iberoamericana 1.1, 145-201 (1985) · Zbl 0704.49005
[34] Willem, M.: Minimax theorems. (1996) · Zbl 0856.49001