system of differential equations first order

... 2011:16 http://www.boundaryvalueproblems.com/content/2011/1/16 Page 5 of 11 RESEARC H Open Access On the solvability conditions of the first boundary value problem for a system of elliptic equations that strongly degenerate at ... uniqueness of the solutions are obtained. Keywords: systems of elliptic equations, degenerate elliptic equations, boundary value problems, Dirichlet type problem 1 Introduction and statement of the ... stasys. rutkauskas@mii.vu.lt Institute of Mathematics and Informatics of Vilnius University, Akademijos str. 4, LT-08863, Vilnius, Lithuania Abstract A system of elliptic equations which are irregularly...

Ngày tải lên: 21/06/2014, 00:20

... polynomial solutions of a class of linear differential equations of the second order. Bull A M S. 36, 77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0 Azad et al. Advances in Difference Equations 2011, ... Advances in Difference Equations 2011, 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 3 of 12 RESEARCH Open Access Polynomial solutions of differential equations H Azad * , ... which is an eigenfunction of L. Specializing to second -order equations because of their importance in applications– and leaving in this article the higher -order case because of its technical complexity–the canonical...

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... example, we will obtain the bound of the solutions of an integral equation. For the sake of proving the global existence of solutions of differential equations, we first recall some basic facts. ... present two examples in order to illustrate the validity of the above results. In the first example, we will try to prove the global existence of the solu- tions of a delay differential equation, ... integral equation, differential equa- tion, bounded 1 Introduction During the past decades, with the development of the theory of differential and integral equations, a lot of integral inequalities,...

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... some of those systems can be reduced to some Ricatti equations or to some previously studied second -order rational equations. Further, since, for some choices of the parameters, one obtains a system which ... argument θ of the complex root is a rational multiple of π, the system is globally periodic. 4.4. Stability of Fixed Points We finish this section with the complete study of the stability of the fixed ... attention on three aspects of the dynamics of the system: the boundedness character and asymptotic behavior of its solutions, the existence of periodic orbits in particular, of prime period-two solutions,...

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... Difference Equations 2011, 2011:14 http://www.advancesindifferenceequations.com/content/2011/1/14 Page 14 of 17 RESEARCH Open Access Some new results for BVPs of first- order nonlinear integro -differential ... the existence of solutions for first- order nonlinear integro -differential equations with boundary value conditions. Our methods to prove the existence of solutions involve new differential inequalities and ... for first order impulsive integro -differential equations of mixed type. J Math Anal Appl. 296,8–20 (2004). doi:10.1016/j.jmaa.2003.12.047 8. Jankowski, T, Jankowski, R: On integro -differential equations...

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... Trujillo JJ: Differential equations of fractional order: methods, results and problem. I Appl Anal 2001, 78:153-192. 6. Kilbas AA, Trujillo JJ: Differential equations of fractional order: methods, ... uniqueness of solutions for coupled systems of higher -order nonlinear fractional differential equations. Fixed Point Theory Appl 2010, 2010:1-17. 30. Babakhani A: Positive solutions for system of nonlinear ... of author information is available at the end of the article Abstract In this article, we study the existence of positive solutions for a coupled system of nonlinear differential equ ations of...

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... solutions), unfortunately often identified in the literature on lower and upper solutions. First- order differential equations with state-dependent deviated argu- ments have received a lot of attention in ... compact set of fixed points in C(I), which are exactly the solutions of problem (4). Claim 2: Every solution x of (4) satisfies α ≤ x ≤ β on I and, therefore, it is a solution of (1) in [α, β]. First, ... [2–7] which deal with existence results for this kind of prob- lems. For the qualitative study of this type of problems we can cite the survey of Hartung et al. [8] and references therein. As main...

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... a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei He (hexiaofei525@sina.com) ISSN ... for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R. China 2 College of Mathematics ... of Lyapunov. Am. J. Math. 73, 885–890 (1951) [3] Cheng, SS: Lyapunov inequalities for differential and difference equations. Fasc. Math. 23, 25–41 (1991) [4] He, Z: Existence of two solutions of...

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... tends to zero as t đ . Proof. The proof of the corollary is similar to the proof of Corollary 3.3 and so it is omitted. From the above results on the oscillation of odd -order differential equation ... delay differential equations of higher order for p(t) = ± 1. Arch Math. 40, 359–366 (2004) 16. Tang, S, Li, T, Thandapani, E: Oscillation of higher -order half-linear neutral differential equations. ... On the oscillation of odd order neutral differential equations. Fasc Math. 29, 167–183 (1999) 21. Zhang, Q, Yan, J: Oscillation behavior of even order neutral differential equations with variable...

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... infinite systems of differential functional equations and strongly coupled infinite systems of first order partial differential equations. Rocky Mt J Math. 10, 237–246 (1980) Kamont Journal of Inequalities ... in the theory of first- order partial differential equations, including questions such as estimates of solutions of initial problems, estimates of domains of solutions, estimates of the difference ... Functional differential inequalities, Haar pyramid, Comparison the orems, Weak solutions of initial problems 1 Introduction Two types of results on first- order partial differential or functional differential...

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... applications of integer order differential equations wit h deviat ed arguments, we refer the reader to the refer- ences [39-45]. As far as we know, fractional order differential equations with ... some nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first- order impulsive differential equations with advanced ... Difference Equations 2011, 2011:2 http://www.advancesindifferenceequations.com/content/2011/1/2 Page 6 of 11 44. Wang G, Zhang L, Song G: Integral boundary value problems for first order integro-differential...

Ngày tải lên: 21/06/2014, 03:20

... solutions of the integer -order equations are found to follow as special cases of those of fractional -order equations. We consider the system of fractional -order equations of the form D α i y i  t   ... kinds of nonlinear equations. The new homotopy perturbation method NHPM was applied to linear and nonlinear ODEs 17. In this paper, we construct the solution of system of fractional -order ... pY i,1  −L −1 i  ∞  n0 a i,n P n  t   . 3.10 Equating the coefficients of like powers of p, we get the following set of equations: coefficient of p 0 : Y 0  L −1  ∞  n0 a i,n P n  t   , coefficient of p 1 : Y 1  L −1 i  f i  ...

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... differential equations, ” Applicable Analysis, vol. 87, no. 7, pp. 851–863, 2008. 7 V. D. Gejji, “Positive solutions of a system of non-autonomous fractional differential equations, ” Journal of Mathematical ... class of four-point nonlocal boundary value problem of nonlinear integrodifferential equations of fractional order by applying some fixed point theorems. On the other hand, impulsive differential equations ... Section 2. To the best of our knowledge, this is the first time in the literatures that a nonlocal boundary value problem of impulsive differential equations of fractional order is considered. ...

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... delay dynamic equations of first order, ” Advances in Difference Equations, vol. 2008, Article ID 458687, 12 pages, 2008. 10 H. A. Agwo, “On the oscillation of first order delay dynamic equations with ... uniqueness of solutions to systems of delay dynamic equations on time scales,” http://arxiv.org/abs/1001.0737v3 . 6 M. Bohner, “Some oscillation criteria for first order delay dynamic equations, ” ... Article Nonoscillation of First- Order Dynamic Equations with Several Delays Elena Braverman 1 and Basáak Karpuz 2 1 Department of Mathematics and Statistics, University of Calgary, 2500 University...

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... and Lyapunov Stability of Periodic Solutions for Generalized Higher -Order Neutral Differential Equations Jingli Ren, 1 Wing-Sum Cheung, 2 and Zhibo Cheng 1 1 Department of Mathematics, Zhengzhou ... 1.3 into a system of first -order differential equations, and then by applying Mawhin’s continuation theory and some new inequalities, we obtain sufficient conditions for the existence of periodic ... kind of second order neutral functional differential equations, ” Applied Mathematics and Computation, vol. 190, no. 2, pp. 1394–1401, 2007. 7 Q. Wang and B. Dai, “Three periodic solutions of nonlinear...

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