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)
Positive periodic solutions of delayed differential equations. (English) Zbl 1248.34104

Summary: In this paper, we are concerned with the existence, multiplicity and nonexistence of positive ?-periodic solutions of the following equation

u '' (t)+a(t,u)u(t)=λb(t)f(u(t-τ(t))),t,

where a(·,·)C(×, + ) is a ω-periodc function with respect to the first variable, b(·)C(,[0,)), τ(·)C(,) are ω-periodic functions, fC([0,),[0,)) and f(s)>0 for s>0, λ>0 is a parameter. The proof of our main result is based upon fixed point index theory.

34K13Periodic solutions of functional differential equations
47N20Applications of operator theory to differential and integral equations
[1]Chu, J.; Torres, P. J.; Zhang, M.: Periodic solution of second order non-autonomous singular dynamical systems, J. differ. Eqs. 239, 196-212 (2007) · Zbl 1127.34023 · doi:10.1016/j.jde.2007.05.007
[2]Franco, D.; Torres, P. J.: Periodic solution of singular systems without the strong force condition, Proc. am. Math. soc. 136, 1229-1236 (2008) · Zbl 1129.37033 · doi:10.1090/S0002-9939-07-09226-X
[3]Jiang, D.; Chu, J.; Zhang, M.: Multiplicity of positive periodic solution to superlinear repulsive singular equation, J. differ. Eqs. 211, 282-302 (2005) · Zbl 1074.34048 · doi:10.1016/j.jde.2004.10.031
[4]Torres, P. J.; Zhang, M.: A monotone scheme for a nonlinear second order equation based on a generalized anti-maximum principle, Mathematische nachrichten 251, 101-107 (2003) · Zbl 1024.34030 · doi:10.1002/mana.200310033
[5]Freedman, H. I.; Wu, J.: Periodic solutions of single-species models with periodic delay, SIAM J. Math. anal. 23, 689-701 (1992) · Zbl 0764.92016 · doi:10.1137/0523035
[6]Wu, J.; Wang, Z.: Positive periodic solutions of second-order nonlinear differential systems with two parameters, Comput. math. Appl. 56, 43-54 (2008) · Zbl 1145.34333 · doi:10.1016/j.camwa.2007.07.017
[7]Cheng, S.; Zhang, G.: Existence of positive periodic solutions for non-autonomous functional differential equations, Electron. J. Differ. eqs. 59, 1-8 (2001) · Zbl 1003.34059 · doi:emis:journals/EJDE/Volumes/2001/59/abstr.html
[8]Torres, P. J.: Existence of one-signed periodic solution of some second order differential equations via a Krasnoselskii fixed point theorem, J. differ. Eqs. 190, 643-662 (2003) · Zbl 1032.34040 · doi:10.1016/S0022-0396(02)00152-3
[9]R.Y. Ma, C.H. Gao, R.P. Chen, Existence of positive solutions of nonlinear second-order periodic boundary value problems, Boundary value problems, Article ID 626054, p. 18, 2010. · Zbl 1219.34055 · doi:10.1155/2010/626054
[10]Guo, C. J.; Guo, Z. M.: Existence of multiple periodic solutions for a class of second-order delay differential equations, Nonlinear anal. Real world appl. 10, 3285-3297 (2009) · Zbl 1190.34083 · doi:10.1016/j.nonrwa.2008.10.023
[11]Ye, D.; Fan, M.; Wang, H.: Periodic solutions for scalar functional differential equations, Nonlinear anal. 62, 1157-1181 (2005) · Zbl 1089.34056 · doi:10.1016/j.na.2005.03.084
[12]Li, Y.; Fan, X.; Zhao, L.: Positive periodic solutions of functional differential equations with impulses and a parameter, Comput. math. Appl. 56, 2556-2560 (2008) · Zbl 1165.34401 · doi:10.1016/j.camwa.2008.05.007
[13]Jin, Z. L.; Wang, H. Y.: A note on positive periodic solutions of delayed differential equations, Appl. math. Lett. 23, 581-584 (2010) · Zbl 1194.34130 · doi:10.1016/j.aml.2010.01.015
[14]M. Zhang, Optimal conditions for maximum and antimaximum principle of the periodic solutions problem, Boundary value problems, Article ID 410986, p. 26, 2010. · Zbl 1200.34001 · doi:10.1155/2010/410986
[15]Wang, H. Y.: Positive periodic solutions of functional differential systems, J. differ. Eqs. 202, 354-366 (2004) · Zbl 1064.34052 · doi:10.1016/j.jde.2004.02.018