# 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)
Existence and uniqueness of periodic solutions for a kind of Rayleigh equation with two deviating arguments. (English) Zbl 1145.34038

Summary: We consider a class of Rayleigh equations with two deviating arguments of the form

${x}^{\text{'}\text{'}}+f\left(t,{x}^{\text{'}}\left(t\right)\right)+{g}_{1}\left(t,x\left(t-{\tau }_{1}\left(t\right)\right)\right)+{g}_{2}\left(t,x\left(t-{\tau }_{2}\left(t\right)\right)\right)=p\left(t\right)·$

By using the coincidence degree theory, we establish new results on the existence and uniqueness of periodic solutions for the above equation.

##### MSC:
 34K13 Periodic solutions of functional differential equations
##### References:
 [1] Burton, T. A.: Stability and periodic solution of ordinary and functional differential equations, (1985) · Zbl 0635.34001 [2] Xiong, Wanmin; Zhou, Qiyuan; Xiao, Bing; Wang, Yixuan; Long, Fei: Periodic solutions for a kind of Liénard equation with two deviating arguments, Nonlinear anal. Real world appl. 8, No. 3, 787-796 (2007) · Zbl 1136.34056 · doi:doi:10.1016/j.nonrwa.2006.03.004 [3] Mawhin, J.: Periodic solutions of some vector retarded functional differential equations, J. math. Anal. appl. 45, 588-603 (1974) · Zbl 0275.34070 · doi:doi:10.1016/0022-247X(74)90053-5 [4] Gaines, R. E.; Mawhin, J.: Coincide degree and nonlinear differential equations, Lecture notes in math. 568 (1977) · Zbl 0339.47031 [5] Lu, Shiping; Ge, Weigao: Periodic solutions for a kind of liéneard equations with deviating arguments, J. math. Anal. appl. 249, 231-243 (2004) · Zbl 1054.34114 · doi:doi:10.1016/j.jmaa.2003.09.047 [6] Lu, Shiping; Ge, Weigao: Some new results on the existence of periodic solutions to a kind of Rayleigh equation with a deviating argument, Nonlinear anal. 56, 501-514 (2004) · Zbl 1078.34048 · doi:doi:10.1016/j.na.2003.09.021 [7] Xiankai, Huang; Xiang, Z. G.: On existence of $2\pi$-periodic solutions for delay Duffing equation x”+g(t,x(t-$\tau \left(t\right)\right)\right)=p\left(t\right)$, Chinese sci. Bull. 39, 201-203 (1994) · Zbl 0810.34066 [8] Wang, Genqiang: A priori bounds for periodic solutions of a delay Rayleigh equation, Appl. math. Lett. 12, 41-44 (1999) · Zbl 0980.34068 · doi:doi:10.1016/S0893-9659(98)00169-4 [9] Liu, Bingwen; Huang, Lihong: Periodic solutions for a class of forced Liénard-type equations, Acta math. Appl. sin. Engl. ser. 21, 81-92 (2005) · Zbl 1093.34020 · doi:doi:10.1007/s10255-005-0218-y [10] Huang, Chuangxia; He, Yigang; Huang, Lihong; Tan, Wen: New results on the periodic solutions for a kind of Rayleigh equation with two deviating arguments, Math. comput. Modelling 46, No. 5–6, 604-611 (2007) · Zbl 1161.34345 · doi:doi:10.1016/j.mcm.2006.11.024 [11] Zhou, Qiyuan; Long, Fei: Existence and uniqueness of periodic solutions for a kind of Liénard equation with two deviating arguments, J. comput. Appl. math. 206, No. 2, 1127-1136 (2007) · Zbl 1122.34051 · doi:doi:10.1016/j.cam.2006.09.013 [12] Hardy, G. H.; Littlewood, J. E.; Polya, G.: Inequalities, (1964)