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Grimm, L. J.; Schmitt, K.

Boundary value problems for differential equations with deviating arguments. (English) Zbl 0198.13201

Aequationes Math. 4, 176-190 (1970).
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Cited in 25 Documents

Keywords:

ordinary differential equations
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References:

[1] Aliev, R. M.,On a Boundary Value Problem for Second Order Linear Differential Equations with Retarded Argument (Russian), inProc. Second Scientific Conference at Moscow’s People’s Friendship University (1966), pp. 15–16.
[2] Driver, R. D.,Existence and Stability of Solutions of a Delay-Differential System, Arch. Rational Mech. Anal.10, 401–426 (1962). · Zbl 0105.30401 · doi:10.1007/BF00281203
[3] –,Existence Theory for a Delay-Differential System, Contrib. Diff. Equations1, 317–336 (1963).
[4] –,Existence and Continuous Dependence of Solutions of a Neutral Functional-Differential Equation, Arch. Rational Mech. Anal.19, 149–166 (1965). · Zbl 0148.05703 · doi:10.1007/BF00282279
[5] Dunford N. andSchwartz, J.,Linear Operators, Part I:General Theory (Interscience, New York 1958).
[6] El’sgol’ts, L. E.,Introduction to the Theory of Differential Equations with Deviating Arguments (Holden-Day, San Francisco 1966).
[7] Grimm, L. J., andSchmitt, K.,Boundary Value Problems for Delay-Differential Equations, Bull. Amer. Math. Soc.74, 997–1000 (1968). · Zbl 0167.38504 · doi:10.1090/S0002-9904-1968-12114-7
[8] Hartman, P.,Ordinary Differential Equations (Wiley, New York 1964). · Zbl 0125.32102
[9] Jackson, L. K. andSchrader, K.,Comparison Theorems for Nonlinear Differential Equations, J. Differential Equations3, 248–255 (1967). · Zbl 0149.29701 · doi:10.1016/0022-0396(67)90029-0
[10] Jackson, L. K.,Subfunctions and Boundary Value Problems for Second Order Ordinary Differential Equations, Advances in Math.2, 307–363 (1968). · Zbl 0197.06401 · doi:10.1016/0001-8708(68)90022-4
[11] G. A. Kamenskii,Boundary Value Problems for Nonlinear Equations with Perturbed Arguments (Russian), Nauk-Dokl. Vyssh. Shkoly Fiz. Mat. Nauki2, 60–66 (1958).
[12] –,Boundary Value Problems for Nonlinear Differential Equations with Deviating Arguments of Neutral Type (Russian), Trudy Sem. Teor. Diff. Urav. Otklon. Arg.1, 47–51 (1962).
[13] –,On Uniqueness of Solutions of Boundary Value Problems for Nonlinear Second Order Differential Equations with Deviating Arguments of Neutral Type (Russian),ibid. 4, 274–277 (1967).
[14] –, andEl’sgol’ts, L. E.,Some Directions of Investigation on the Theory of Differential Equations with Deviating Argument (Russian),ibid. 6, 3–36 (1968).
[15] Knobloch, H. W.,Eine neue Methode zur Approximation periodischer Lösungen nicht-linearer Differentialgleichungen zweiter Ordnung, Math. Z.82, 177–197 (1962). · Zbl 0117.05404 · doi:10.1007/BF01111422
[16] Martynjuk, D. I.,Periodic Solutions of Nonlinear Second Order Differential Equations with Retarded Arguments (Russian), Ukrain. Mat. Žh.19, 125–132 (1967).
[17] Mikolajska, Z.,Une remarque sur l’existence d’une solution périodique d’une équation différo-différentielle aux deuxième membre croissant, Ann. Polon. Mat.18, 53–58 (1966). · Zbl 0154.33903
[18] Myshkis, A. D., andEl’sgol’ts, L. E.,Some Results and Problems in the Theory of Differential Equations, Uspehi Mat. Nauk,22, 21–57 (1967) = Russian Math. Surveys22, 19–57 (1967). · Zbl 0189.40001
[19] Norkin, S. B.,On a Boundary Value Problem for a Second Order Differential Equation with a Retarded Argument on a Half-Axis (Russian), Trudy Sem. Diff. Urav. Otklon. Arg.2, 162–171 (1963).
[20] –,Second Order Differential Equations with Retarded Argument (Russian) (Nauka, Moscow 1965).
[21] Schmitt, K.,Periodic Solutions of Nonlinear Second Order Differential Equations, Math. Z.98, 200–207 (1967). · Zbl 0153.12501 · doi:10.1007/BF01112414
[22] –,Boundary Value Problems for Nonlinear Second Order Differential Equations, Monatsh. Math.72, 374–354 (1968). · Zbl 0162.11502 · doi:10.1007/BF01302169
[23] –,Bounded Solutions of Nonlinear Second Order Differential Equations, Duke Math. J.36, 2 (1969). · Zbl 0182.12001 · doi:10.1215/S0012-7094-69-03630-8
[24] Schrader, K. W.,Boundary Value Problems for Second-Order Ordinary Differential Equations. J. Differential Equations3, 403–413 (1967). · Zbl 0152.28401 · doi:10.1016/0022-0396(67)90040-X
[25] Zverkin, A. M., Kamenskii, G. A., Norkin, S. B., andEl’sgol’ts, L. E.,Differential Equations with a Perturbed Argument, Uspehi Mat. Nauk. 17, 77–164 (1962) = Russian Math. Surveys17, 61–146 (1962).
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