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)
Homoclinic solutions for a class of nonperiodic and noneven second-order Hamiltonian systems. (English) Zbl 1246.37084
Summary: The existence of homoclinic solutions is obtained for second-order Hamiltonian systems -u ¨(t)+L(t)u(t)=W(t,u(t))-f(t), as the limit of the solutions of a sequence of nil-boundary-value problems which are obtained by the mountain pass theorem, when L(t) and W(t,x) are neither periodic nor even with respect to t.

MSC:
37J45Periodic, homoclinic and heteroclinic orbits; variational methods, degree-theoretic methods
References:
[1]Ambrosetti, A.; Zelati, Vittorio Coti: Multiple homoclinic orbits for a class of conservative systems, Rend. sem. Mat. univ. Padova 89, 177-194 (1993) · Zbl 0806.58018 · doi:numdam:RSMUP_1993__89__177_0
[2]Carrião, P. C.; Miyagaki, O. H.: Existence of homoclinic solutions for a class of time-dependent Hamiltonian systems, J. math. Anal. appl. 230, No. 1, 157-172 (1999) · Zbl 0919.34046 · doi:10.1006/jmaa.1998.6184
[3]Ding, Y.; Li, S. J.: Homoclinic orbits for first order Hamiltonian systems, J. math. Anal. appl. 189, No. 2, 585-601 (1995) · Zbl 0818.34023 · doi:10.1006/jmaa.1995.1037
[4]Felmer, Patricio L.; De B. Silva, Elves A.: Homoclinic and periodic orbits for Hamiltonian systems, Ann. sc. Norm. super. Pisa cl. Sci. (4) 26, No. 2, 285-301 (1998) · Zbl 0919.58026 · doi:numdam:ASNSP_1998_4_26_2_285_0
[5]Izydorek, M.; Janczewska, J.: Homoclinic solutions for a class of the second order Hamiltonian systems, J. differential equations 219, No. 2, 375-389 (2005) · Zbl 1080.37067 · doi:10.1016/j.jde.2005.06.029
[6]Izydorek, M.; Janczewska, J.: Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential, J. math. Anal. appl. 335, No. 2, 1119-1127 (2007) · Zbl 1118.37032 · doi:10.1016/j.jmaa.2007.02.038
[7]Korman, P.; Lazer, A. C.: Homoclinic orbits for a class of symmetric Hamiltonian systems, Electron. J. Differential equations 1994, No. 1, 1-10 (1994)
[8]Lv, Y.; Tang, C. -L.: Existence of even homoclinic orbits for second-order Hamiltonian systems, Nonlinear anal. 67, No. 7, 2189-2198 (2007) · Zbl 1121.37048 · doi:10.1016/j.na.2006.08.043
[9]Ou, Z. Q.; Tang, C. -L.: Existence of homoclinic solution for the second order Hamiltonian systems, J. math. Anal. appl. 291, No. 1, 203-213 (2004) · Zbl 1057.34038 · doi:10.1016/j.jmaa.2003.10.026
[10]Paturel, Eric: Multiple homoclinic orbits for a class of Hamiltonian systems, Calc. var. Partial differential equations 12, No. 2, 117-143 (2001) · Zbl 1052.37049 · doi:10.1007/s005260000048
[11]Rabinowitz, P. H.: Homoclinic orbits for a class of Hamiltonian systems, Proc. roy. Soc. Edinburgh sect. A 114, No. 1 – 2, 33-38 (1990) · Zbl 0705.34054 · doi:10.1017/S0308210500024240
[12]Rabinowitz, P. H.; Tanaka, K.: Some results on connecting orbits for a class of Hamiltonian systems, Math. Z. 206, No. 3, 473-499 (1991) · Zbl 0707.58022 · doi:10.1007/BF02571356
[13]Tang, X. H.; Xiao, L.: Homoclinic solutions for a class of second order Hamiltonian systems, Nonlinear anal. 71, No. 3 – 4, 1140-1152 (2009) · Zbl 1185.34056 · doi:10.1016/j.na.2008.11.038
[14]Tang, X. H.; Xiao, L.: Homoclinic solutions for nonautonomous second-order Hamiltonian systems with a coercive potential, J. math. Anal. appl. 351, No. 2, 586-594 (2009) · Zbl 1153.37408 · doi:10.1016/j.jmaa.2008.10.038