zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
Solutions for a quasilinear Schrödinger equation: a dual approach. (English) Zbl 1035.35038
The authors develop a variational approach in $H^1(\bbfR^N)$ for proving the existence of solutions of a quasilinear stationary Schrödinger equation. This is achieved by means of a suitable change of variables for transforming the problem into an equation of a semilinear elliptic type to which one applies the Mountain Pass geometry.

MSC:
35J60Nonlinear elliptic equations
47J30Variational methods (nonlinear operator equations)
35J20Second order elliptic equations, variational methods
WorldCat.org
Full Text: DOI
References:
[1] Berestycki, H.; Gallouët, T.; Kavian, O.: Equations de champs scalaires euclidiens non linéaires dans le plan. CR acad. Sci. Paris ser. I math. 297, No. 5, 307-310 (1983)
[2] Berestycki, H.; Lions, P. L.: Nonlinear scalar field equations I. Arch. rational mech. Anal. 82, 313-346 (1983) · Zbl 0533.35029
[3] Brizkik, L.; Eremko, A.; Piette, B.; Zakrzewski, W. J.: Electron self-trapping in a discrete two-dimensional lattice. Physica D 159, 71-90 (2001) · Zbl 0983.81533
[4] Colin, M.: Stability of standing waves for a quasilinear Schrödinger equation in space dimension 2. Adv. differential equations 8, No. 1, 1-28 (2003) · Zbl 1042.35074
[5] Zelati, V. Coti; Rabinowitz, P. H.: Homoclinic type solutions for a semilinear elliptic PDE on RN. Commun. pure appl. Math. 14, 1217-1269 (1992) · Zbl 0785.35029
[6] Ekeland, I.: Convexity methods in Hamiltonian mechanics. (1990) · Zbl 0707.70003
[7] Liu, J. -Q.; Wang, Z. -Q.: Soliton solutions for quasilinear Schrödinger equations. Proc. amer. Math. soc. 131, 441-448 (2003) · Zbl 1229.35269
[8] Liu, J. -Q.; Wang, Y. -Q.; Wang, Z. -Q.: Soliton solutions for quasilinear Schrödinger equations, II. J. differential equation 187, 473-493 (2003) · Zbl 1229.35268
[9] Jeanjean, L.; Tanaka, K.: A remark on least energy solutions in RN. Proc. amer. Math. soc. 131, 2399-2408 (2003) · Zbl 1094.35049
[10] L. Jeanjean, K. Tanaka, A note on a mountain pass characterization of least energy solutions, Adv. Nonlinear Studies, to appear. · Zbl 1095.35006
[11] Lions, P. L.: The concentration-compactness principle in the calculus of variations. The locally compact case. Part I and II. Ann. inst. H. Poincaré, anal. Non lineaire 1, 109, 145 and 223.283 (1984)
[12] Poppenberg, M.; Schmitt, K.; Wang, Z. -Q.: On the existence of soliton solutions to quasilinear Schrödinger equations. Calc. var. 14, 329-344 (2002) · Zbl 1052.35060