systems of differential equations second order

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... be applied to concrete partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution equations one is an integro-differential equation ... properly cited. By using the multiplier technique, we prove that the energy of a system of two coupled second order evolution equations one is an integro-differential equation decays exponentially ... Article Exponential Stability of Two Coupled Second- Order Evolution Equations Qian Wan and Ti-Jun Xiao Shanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences, Fudan...

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... equal to I. The proof of uniqueness is complete. To prove the existence we note, first of all, that it suffices to provide a proof if one of the κ i ’s is equal to ±1 and one of the δ j ’s is equal ... for all k ∈ Z. The proof of the first part of Theorem 4.9 is complete. In order to prove Theorem 4.9(ii), we need to compare the first and the third factors of the two sides of (4.7). The first factors ... solutions of isomonodromy problems for such systems of difference equations. In the case of one-interval gap probability this has been done (in a different language) in [Bor], [BB]. One example of the...

Ngày tải lên: 14/02/2014, 17:20

... 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, ... 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 ... Advances in Difference Equations 2011, 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 6 of 12 3 Canonical forms of self-adjoint second- order equations with polynomial coefficients Let...

Ngày tải lên: 20/06/2014, 22:20

... second 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 ... 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, while in the second ... 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,...

Ngày tải lên: 21/06/2014, 01:20

... Article Approximation of Solutions for Second- Order m-Point Nonlocal Boundary Value Problems via the Method of Generalized Quasilinearization Ahmed Alsaedi Department of Mathematics, Faculty of Science, ... Zuo, “On monotone method for first and second order periodic boundary value problems and periodic solutions of functional differential equations, ” Journal of Mathematical Analysis and Applications, ... the method of generalized quasilinearization to obtain a sequence of approximate solutions converging monotonically and quadratically to a unique solution of the following second- order m−point...

Ngày tải lên: 21/06/2014, 11:20

... oscillation of solutions of first order delay difference equations, ” Cubo, vol. 7, no. 2, pp. 223–236, 2005. 14 R. Medina and M. Pituk, “Nonoscillatory solutions of a second- order difference equation of ... derived for all the solutions being oscillating for a class of linear second- order delayed-discrete equations. We consider the delayed second- order linear discrete equation Δx  n   −p  n  x  n ... Article Oscillation of Solutions of a Linear Second- Order Discrete-Delayed Equation J. Ba ˇ stinec, 1 J. Dibl ´ ık, 1, 2 and Z. ˇ Smarda 1 1 Department of Mathematics, Faculty of Electrical Engineering...

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... Article Multiple Positive Solutions of a Singular Emden-Fowler Type Problem for Second- Order Impulsive Differential Systems Eun Kyoung Lee and Yong-Hoon Lee Department of Mathematics, Pusan National ... 3-4, pp. 307– 328, 2004. 4 B. Liu and J. Yu, “Existence of solution of m-point boundary value problems of second- order differential systems with impulses,” Applied Mathematics and Computation, ... Liu, L. Hu, and Y. Wu, “Positive solutions of two-point boundary value problems for systems of nonlinear second- order singular and impulsive differential equations, ” Nonlinear Analysis: Theory, Methods...

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Ngày tải lên: 14/03/2014, 13:20

... questions of solvability of basic boundary value problems for quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, and also to the investigation of differential ... with this, one of the first questions of the general theory of boundary value problems for quasilinear elliptic equations of the form (1)is the question of distinguishing classes of equations for ... the proof of an a priori estimate of the Hdlder norm IIulIc^(u) for solutions of uniformly elliptic equations. V. The estimate of maxnl vul for equations with structure described in terms of the...

Ngày tải lên: 31/05/2014, 01:37

... is just the repetition of the proof of Lemma 3.2, we omit the details of its proof. With the aid of above preparations, now we will give the proof of Theorem 1.2. Proof of Theorem 1.2 By(1.8), ... similar to the proof of Lemma 3.1, so we omit the details of its proof. Lemma 3.4 Under the conditions of Theorem 1.2, F (x) satisfies the PS condition. Proof From the proof of Lemma 3.2, we see ... non-trivial. Although the proof of the first part of Theorem 1.2 is very similar to the proof of Theorem 1.1, for readers’ convenience, we give its complete proof. Lemma 3.3 Under the conditions of Theorem 1.2,...

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