second order elliptic systems of differential equations

Ngày tải lên: 22/06/2014, 22:20

... to zero as t ® ∞. 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 ... criteria for second- order superlinear neutral differential equations. Abstr Appl Anal. 2011,1–17 (2011) 13. Li, T, Han, Z, Zhao, P, Sun, S: Oscillation of even -order neutral delay differential equations. ... 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. ...

Ngày tải lên: 20/06/2014, 22:20

... independent of . Hindawi Publishing Corporation Boundary Value Problems Volume 2011, Article ID 845413, 18 pages doi:10.1155/2011/845413 Research Article Lagrangian Stability of a Class of Second- Order ... Boundary Value Problems 2. The Proof of Theorem The proof of Theorem 1.1 is based on Moser’s small twist theorem for reversible mapping. It mainly consists of two steps. The first one is to find ... transformations, we change the systems 1.9 to a form of small perturbation of integrable reversible system. Then a KAM Theorem f or reversible mapping can be applied to the Poincar ´ e mapping of this nearly...

Ngày tải lên: 21/06/2014, 07:20

... and Green’s Functions for Boundary Value Problems of Second- Order Four-Point Functional Difference Equations Yang Shujie and Shi Bao Institute of Systems Science and Mathematics, Naval Aeronautical ... theory, Deng and Shi 5 studied the existence and multiplicity of the boundary value problems to a class of second- order functional difference equations Lu n  f  n, u n1 ,u n ,u n−1  1.1 with boundary ... existence of positive solutions for a second- order functional difference equation with four-point boundary conditions. 1. Introduction In recent years, boundary value problems BVPs of differential...

Ngày tải lên: 21/06/2014, 11:20

... nonoscillation of forced second order dynamic equations, ” Pacific Journal of Mathematics, vol. 230, no. 1, pp. 59–71, 2007. 12  M. Bohner and S. H. Saker, “Oscillation of second order nonlinear dynamic equations ... for second- order forced dynamic equations with mixed nonlinearities,” Advances in Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009. 8 D. R. Anderson, “Oscillation of second- order ... second- order nonlinear dynamic equations on time scales,” Electronic Journal of Differential Equations, no. 145, pp. 1–8, 2006. 17 Q. Kong, “Interval criteria for oscillation of second- order...

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Ngày tải lên: 06/07/2014, 15:18

... 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

... follows from ( 1 ) which are appeared in the proof of Theorem 1.2. Then the proof of Theorem 1.3 is completed. □ Proof of Theorem 1.4. From the proof of Theorem 1.1, we know that  is coercive which ... non-autonomous second- order systems with linear nonlinearity. Nonlinear Anal. 60, 325–335 (2005) 12. Wang, Z, Zhang, J: Periodic solutions of a class of second order non-autonomous Hamiltonian systems. Nonlinear ... completes the proof. □ 3 Proof of main results For the sake of convenience, we will denote various positive constants as C i , i =1,2, 3, Now, we are ready to proof our main results. Proof of Theorem...

Ngày tải lên: 21/06/2014, 00:20

... 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

... relationships between the second- order contingent derivative of a set-valued map and its profile map are obtained. By virtue of the second- order contingent derivatives of set-valued maps, some ... the second- order contingent derivative of a set-valued map and its profile map. In Section 4, by the second- order contingent derivative, we discuss the quantitative information on the behavior of ... by virtue of the higher order derivatives or epiderivatives introduced by the higher Fixed Point Theory and Applications 3 order tangent sets. To the best of our knowledge, second- order c ontingent...

Ngày tải lên: 21/06/2014, 05:20

... problem for second order nonlinear singular differential equations, ” Georgian Mathematical Journal, vol. 7, no. 1, pp. 133–154, 2000. 9 Z. Yang, “Positive solutions to a system of second- order nonlocal ... for Fourth -Order Singular p-Laplacian Differential Equations with Integral Boundary Conditions Xingqiu Zhang 1, 2 and Yujun Cui 3 1 Department of Mathematics, Huazhong University of Science and ... a k  r 2   b k a k H k  t, s  x  s  ds. 2.36 By the proof of Lemma 2.3, xt is a solution of problem 2.35 ifandonlyifitisthe fixed point of the following operator equation: x  t    A k  ϕ −1 p  B k F k   x  t  ....

Ngày tải lên: 21/06/2014, 11:20

... Singular Differential Equations It is the goal of the present section to establish a theorem on existence of solutions for 1.1 between a pair of well-ordered lower and upper solutions and in lack of ... solutions of first -order singular differential equations, ” Bulletin of the London Mathematical Society, vol. 40, no. 1, pp. 143–150, 2008. 17 J. Chu and J. J. Nieto, “Recent results for second order ... Solutions Another modification of the concepts of lower and upper solutions concerns the possibility of allowing jumps in their graphs. Since the task of finding a pair of lower and upper solutions is...

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Ngày tải lên: 23/06/2014, 01:20

... 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

... 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...

Ngày tải lên: 21/06/2014, 11:20

... Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department of Mathematics, Harbin Institute of ... Dosly The spectrum containment of almost periodic solution of second- order neutral delay differential equations with piecewise constant of argument EPCA, for short of the form xtpxt − 1   qx2t ... contradiction. The claim follows. 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second- order differential equations with piecewise constant argument,” Nonlinear...

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