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Second-order differential equations with deviating arguments
Boundary Value Problems volume 2006, Article number: 23092 (2006)
Abstract
This paper deals with boundary value problems for second-order differential equations with deviating arguments. Some sufficient conditions are formulated under which such problems have quasisolutions or a unique solution. A monotone iterative method is used. Examples with numerical results are added to illustrate the results obtained.
References
- 1.
Ding W, Han M, Mi J: Periodic boundary value problem for the second-order impulsive functional differential equations. Computers & Mathematics with Applications 2005,50(3-4):491-507. 10.1016/j.camwa.2005.03.010
- 2.
Jankowski T: Advanced differential equations with nonlinear boundary conditions. Journal of Mathematical Analysis and Applications 2005,304(2):490-503. 10.1016/j.jmaa.2004.09.059
- 3.
Jankowski T: On delay differential equations with nonlinear boundary conditions. Boundary Value Problems 2005,2005(2):201-214. 10.1155/BVP.2005.201
- 4.
Jankowski T: Solvability of three point boundary value problems for second order differential equations with deviating arguments. Journal of Mathematical Analysis and Applications 2005,312(2):620-636. 10.1016/j.jmaa.2005.03.076
- 5.
Jankowski T: Boundary value problems for first order differential equations of mixed type. Nonlinear Analysis 2006,64(9):1984-1997. 10.1016/j.na.2005.07.033
- 6.
Jiang D, Fan M, Wan A: A monotone method for constructing extremal solutions to second-order periodic boundary value problems. Journal of Computational and Applied Mathematics 2001,136(1-2):189-197. 10.1016/S0377-0427(00)00610-5
- 7.
Jiang D, Wei J: Monotone method for first- and second-order periodic boundary value problems and periodic solutions of functional differential equations. Nonlinear Analysis 2002,50(7):885-898. 10.1016/S0362-546X(01)00782-9
- 8.
Jiang D, Weng P, Li X: Periodic boundary value problems for second order differential equations with delay and monotone iterative methods. Dynamics of Continuous, Discrete & Impulsive Systems. Series A 2003,10(4):515-523.
- 9.
Kolmanovskii V, Myshkis A: Introduction to the Theory and Applications of Functional Differential Equations, Mathematics and Its Applications. Volume 463. Kluwer Academic, Dordrecht; 1999:xvi+648.
- 10.
Ladde GS, Lakshmikantham V, Vatsala AS: Monotone Iterative Techniques for Nonlinear Differential Equations, Monographs, Advanced Texts and Surveys in Pure and Applied Mathematics. Volume 27. Pitman, Massachusetts; 1985:x+236.
- 11.
Nieto JJ, Rodríguez-López R: Existence and approximation of solutions for nonlinear functional differential equations with periodic boundary value conditions. Computers & Mathematics with Applications 2000,40(4-5):433-442. 10.1016/S0898-1221(00)00171-1
- 12.
Nieto JJ, Rodríguez-López R: Remarks on periodic boundary value problems for functional differential equations. Journal of Computational and Applied Mathematics 2003,158(2):339-353. 10.1016/S0377-0427(03)00452-7
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Jankowski, T., Szatanik, W. Second-order differential equations with deviating arguments. Bound Value Probl 2006, 23092 (2006). https://doi.org/10.1155/BVP/2006/23092
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Keywords
- Differential Equation
- Partial Differential Equation
- Unique Solution
- Ordinary Differential Equation
- Functional Equation
