# 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)
Bounded solutions for differential equations with reflection of the argument. (English) Zbl 0655.34030
Differential equation with reflection of the argument $x'(t)=f(t,x(t),x(- t)),$ $t\in R$ is studied. Sufficient conditions for the existence, uniqueneness, boundedness and almost perodicity of the solutions are obtained.
 [1] Aftabizadeh, A. R.: Bounded solutions for some gradient type systems. Libertas math. 2, 121-130 (1982) · Zbl 0517.34027 [2] Belova, M. M.: Asymptotic properties of bounded solutions of nonlinear second-order differential equations. Differential equations 12, No. No. 11, 1354-1358 (1976) · Zbl 0374.34024 [3] Corduneanu, C.: Bounded and almost periodic solutions of certain nonlinear elliptic equations. Tohoku math. J. 32, No. No. 2, 265-278 (1980) · Zbl 0443.35027 [4] Corduneanu, C.: On the existence of bounded solutions for a class of second-order differential equations. St. cerc. Mat, (Jasi) MR 22, 5790 (1959) · Zbl 0089.00202 [5] Corduneanu, C.: Bounded and almost periodic solutions of certain nonlinear parabolic equations. Libertas math. 2, 131-139 (1982) · Zbl 0504.35007 [6] Gupta, C. P.: Existence and uniqueness theorems for boundary value problems involving reflection of the argument. Nonlinear anal. 11, No. No. 9, 1075-1083 (1987) · Zbl 0632.34069 [7] Gupta, C. P.: Two-point boundary value problems involving reflection of the argument. Inter. J. Math., math. Sci. 10, No. No. 2, 361-371 (1987) · Zbl 0622.34015 [8] Gupta, C. P.: Boundary value problems for differential equations in Hilbert spaces involving reflection of the argument. J. math. Anal. appl. 128, No. No. 2, 375-388 (1987) · Zbl 0658.34053 [9] Layton, W.: Periodic solutions of nonlinear delay equations. J. math. Anal. appl. 77, 198-204 (1980) · Zbl 0437.34057 [10] Layton, W.: Existence of almost periodic solutions to delay differential equations with Lipschitz nonlinearities. J. differential equations 55, 151-164 (1984) · Zbl 0497.34055 [11] Przeworska-Rolewicz, D.: Equations with transformed argument--an algebraic approch. (1973) · Zbl 0271.47008 [12] Shah, S. M.; Wiener, J.: Reducible functional differential equations. Internat. J. Math. sci. 8, No. No. 1, 1-27 (1985) · Zbl 0576.34059 [13] Silberstein, L.: Solution of the equation f’$(x) = f( 1 x)$. Philos. mag. 30, 185-186 (1940) · Zbl 0026.22304 [14] Wiener, J.: Differential equations with involutions. Differencial’nye uravnenija 6, 1131-1137 (1969) [15] Wiener, J.: Differential equations in partial derivatives with involutions. Differencial’nye uravnenija 7, 1320-1322 (1970) [16] Wiener, J.: Differential equations with periodic transformations of the argument. Izv. vyssh. Uchebn. zaved. Radiofiz. 3, 481-484 (1973) [17] Wiener, J.: Investigation of some functional differential equations with a regular singular point. Differencial’nye uravnenija 10, 1891-1894 (1974) [18] Wiener, J.: On Silberstein’s functional equation. Uchen. zap. Ryazan. pedagog. Inst. 41, 5-8 (1966) [19] Wiener, J.; Aftabizadeh, A. R.: Boundary value problems for differential equations with reflection of the argument. Internat. J. Math. sci. 8, No. No. 1, 151-163 (1985) · Zbl 0583.34055