system of second order differential equations mathematica

... Solutions of Singular Nonautonomous Second- Order Differential Equations Irena Rach ˚ unkov ´ aandJanTome ˇ cek Department of Mathematical Analysis and Applications of Mathematics, Faculty of Science, ... differential equation of a c ˚ the second- order on the half-line,” in Mathematical Models in Engineering, Biology... “Nucleation of spherical shell-like interfaces by second gradient theory: ... here we prove the existence of a homoclinic solution for f having a linear behaviour near −∞. The proof is based on a full description of the set of all solutions of problem 1.1, 1.10 for

Ngày tải lên: 21/06/2014, 20:20

... 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) ... inequalities for a class of even -order differential equations Qi-Ming Zhang∗1 and Xiaofei He2 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R China College of Mathematics ... generalizations of (1.2) in some literatures Especially, Lyapunov inequality has been generalized extensively to the higher -order linear equations and the linear Hamiltonian systems A thorough

Ngày tải lên: 20/06/2014, 21:20

... of the American Mathematical Society, vol 41, pp 110–116, 1973 ˇ a 6 S Matucci and P Reh´ k, Regularly varying sequences and second order difference equations, ” Journal of Difference Equations ... values of the limits at infinity of themselves and of their first difference A classification of. .. for example, 9–12 for a complete treatment including more general equations The aim of ... the study of dominant and recessive solutions Let Advances in Difference Equations 13 R denote the set of all positive recessive solutions of 1.1 and D denote the set of all positive

Ngày tải lên: 21/06/2014, 11:20

... differential equations of second order, ” Annals of Mathematics, vol 65, pp 197–202, 1957 R Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Annals of Differential ... differential equations of second order, ” Proceedings of the American Mathematical Society, vol 13, pp 603–610, 1962 W Leighton, “Some elementary Sturm theory,” Journal of Differential Equations, ... comparison theorem of second- order differential equations see Section Remark 3.6 In the discrete case: μ t ≡ This result is the same as Sturm comparison theorem of second- order difference equations see

Ngày tải lên: 21/06/2014, 20:20

... solutions of semilinear Duffing equations, Journal of Differential Equations 105 (1993), no 2, 364–409 [5] C Fabry and D Fayyad, Periodic solutions of second order differential equations ... SOLUTIONS OF SECOND- ORDER LIÉNARD EQUATIONS WITH p-LAPLACIAN-LIKE OPERATORS YOUYU WANG AND WEIGAO GE Received 12 April 2005; Accepted 10 August 2005 The existence of periodic solutions for second- order ... with one-sided e... for periodic solutions of forced nonlinear second order ordinary differential equations, Bulletin of the London Mathematical Society 18 (1986), no 2, 173–180 [7]

Ngày tải lên: 22/06/2014, 22:20

... (C) To establish the (differential) equations Analysis of the Model (A) To solve equations (B) To find the properties of solutions (C) If it is too difficult to solve the equations, try to approximate ... situation into mathematical terms: (A) To choose the (physical, natural, ) laws governing the problem (B) To choose mathematical variables (C) To establish the (differential) equations Analysis of the ... Series and Differential Equations Nguyen Thieu Huy Hanoi University of Science and Technology Nguyen Thieu Huy (HUST) Infinite Series and Diff Eq 1/9 Exact equations 3.1 Definition A differential

Ngày tải lên: 23/04/2020, 08:00

... Dynamics of Second Order Rational Difference Equations, Chapman & c Hall/CRC, Boca Raton, Fla, USA, 2002 G Ladas, “Invariants for generalized Lyness equations, ” Journal of Difference Equations ... solutions m, M ∈ L, U of either one of the systems of equations M f M, M , m f m, m , M f m, m , m f M, M 3.6 and 3.7 necessarily satisfy m M In either case, the hypotheses i or ii of Theorem 2.1 are ... completes the proof of the lemma Proof of Theorem 1.4 To prove Theorem 1.4 it is enough to assume statement B of Proposition 3.1 Also by Lemma 3.3 we may assume p / q without loss of generality

Ngày tải lên: 21/06/2014, 20:20

... differential equations of third order, ” ¸ Nonlinear Dynamics and Systems Theory, vol 7, no 4, pp 419–430, 2007 24 C Tunc, “On the nonoscillation of solutions of nonhomogeneous third order differential equations, ” ... Bulletin ¸ of the Greek Mathematical Society, vol 39, pp 131–137, 1997 26 C Tunc and E Tunc, “On the asymptotic behavior of solutions of certain second- order differential ¸ ¸ equations, ” Journal of the ... solutions of a class of second order functional-differential equations, ” Analysis, vol 13, no 1-2, pp 19–28, 1993 11 N Parhi, “On non-homogeneous canonical third -order linear differential equations, ”

Ngày tải lên: 22/06/2014, 02:20

... Difference equations and systems of difference equations have many applications in bi- ology, economy, and other sciences. So there exist many papers concerning systems of difference equations (see ... 47–59, 1998 [8] C J Schinas, “Invariants for difference equations and systems of difference equations of rational form,” Journal of Mathematical Analysis and Applications, vol 216, no 1, ... Kulenovi´ and Z Nurkanovi´ , “Global behavior of a three-dimensional linear fractional c c system of difference equations, ” Journal of Mathematical Analysis and Applications, vol 310,

Ngày tải lên: 22/06/2014, 19:20

... Trudinger, Elliptic Partial Differential Equations of Second Order, vol 224 of Fundamental Principles of Mathematical Sciences, Springer,... parabolic equations, ” in Harmonic Analysis ... of partial differential equations, it is important to have estimates of solu- tions, which do not depend on the smoothness of the given data. Such kind of estimates include different versions of ... 277 of Contemp Math., pp 87–112, American Mathematical Society, Rhode Island, 2001 [17] V A Kondrat’ev and E M Landis, “Qualitative theory of second- order linear partial differential equations,

Ngày tải lên: 22/06/2014, 22:20

... y(N + 1) 190 Periodic solutions of nonlinear second- order difference equations Solutions of this problem... when the roots of λ1 and λ2 of the characteristic equation λ2 + ... 10.1155/ADE.2005.173 174 Periodic solutions of nonlinear second- order difference equations As a consequence of this result we prove that there is a countable subset S of [ −2,2] such that if b/ ∈S,then ... to know that the columns of Ψ(·) span the solution space of the homogeneous “adjoint” problem  Lx =0, (2.14) 176 Periodic solutions of nonlinear second- order difference equations where  L =X

Ngày tải lên: 23/06/2014, 00:20

... ao In m any te c h n ic a l p ro b le m s we have m et the d iffe re n tia l e q u a tio n s o f second o rd er R e c e n tly , in so m e fields o f P h y sics, M e c h a n ic s a n d B io lo g ... s T h e first p a g p h is co n ce rn e d w ith the a u to n o m o u s e q u a tio n a n d the second o ne — w ith the n o n -a u to n o m o u s e q u atio n S O L U T IO N O F A U T O N O M

Ngày tải lên: 08/04/2015, 15:36

... possible to classify the fourth -order differential equations into two forms: fully order differential equations and non-fully fourth -order ones A fourth-fourth -order differential equation whose right-hand ... problems for differential equations Among the differential equations, the nonlinear fourth -order differential equation has been of great interest recently as it is the mathematical model of many ... reduce a differential problem to a discrete problem on a grid of points leading to solving a linear algebraic system of equations The boundary value problem for the second- order differential equations,

Ngày tải lên: 01/04/2021, 19:17

... a class of higher -order difference equations Huantao Zhu1 and Weibing Wang∗2 Hunan College of Information, Changsha, Hunan 410200, P.R China Department of Mathematics, Hunan University of Science ... periodic solutions of functional discrete systems and population model Adv Differ Equ 2005, 369–380 (2005) [13] Liu, Y: Periodic solutions of second order nonlinear functional difference equations Archivum ... and multiple positive periodic solutions of (1.3) Our aim of this article is to study the existence of periodic solutions for the higherorder difference equations (1.1) using the well-known Schauder’s

Ngày tải lên: 18/06/2014, 22:20

... solutions to first -order differential equations with state-dependent deviated arguments Rub´n Figueroa∗ and Rodrigo L´pez Pouso e o Department of Mathematical Analysis, University of Santiago de Compostela, ... a peculiar feature of equations with deviated arguments, see [1] for an example with a second- order equation Therefore, we are obliged to distinguish between the concepts of minimal solution ... ordinary differential equations with deviated arguments J Optim Theory Appl 135(2), 257–269 (2007) Jankowski, T: Existence of solutions of boundary value problems for differential equations in which

Ngày tải lên: 20/06/2014, 20:20

... Simulation of Large Scale Complex Systems, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210046, PR China Full list of author information is available at the end of the article ... Next we want to derive the decay rate of energy function for problem (1.1). By mul- tiplying the first equation of system (1.1) by u and the second equation of system (1.1) by v, integrating over ... http://www.boundaryvalueproblems.com/content/2011/1/22 Page 10 of 19 [...]... Said-Houari, B, Messaoudi, SA, Guesmia, A: General decay of solutions of a nonlinear system of viscoelastic wave equations Nonlinear

Ngày tải lên: 21/06/2014, 00:20

... second- order Emden-Fowler delay dynamic equations on time scales,” Journal of Mathematical Analysis and Applications, vol 334, no 2, pp 847–858, 2007 13 Y Sahiner, “Oscillation of second- order ... for second- order linear equations on a time scale,” Journal of Difference Equations and Applications, vol 8, no 11, pp 1061–1071, 2002 T S Hassan, “Oscillation criteria for half-linear dynamic equations ... scales,” Journal of Mathematical Analysis and Applications, vol 345, no 1, pp 176–185, 2008 R P Agarwal, M Bohner, and S H Saker, “Oscillation of second order delay dynamic equations, ” The Canadian

Ngày tải lên: 21/06/2014, 05:20

... consists of two steps The first one is to find an equivalent system, which has a nearly integrable form of a reversible system The second one is to show that Pincar´ map of the e equivalent system ... our proof greatly It is easy to see from the proof that this main nonlinearity is used to guarantee the small twist condition 4 Boundary Value Problems The Proof of Theorem The proof of Theorem ... doi:10.1155/2011/845413 Research Article Lagrangian Stability of a Class of Second- Order Periodic Systems Shunjun Jiang, Junxiang Xu, and Fubao Zhang Department of Mathematics, Southeast University, Nanjing

Ngày tải lên: 21/06/2014, 07:20

... 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 ... 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, ... Proof The proof is similar to that of Theorem 4.13 We give the following example as an application of Theorem... 600 800 1000 1200 Figure 2: The graph of 7 iterates for the solutions of

Ngày tải lên: 21/06/2014, 11:20

... Article Limit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach ˚ unkov ´ a, 1 Svatoslav Stan ˇ ek, 1 Ewa Weinm ¨ uller, 2 and Michael Zenz 2 1 Department of Mathematical ... the solvability of nonlinear singular equations subject to different types of boundary conditions. In this section, we utilize Theorem 4.1 to show the existence of solutions for periodic problems. The rest of ... values of the first derivative at the end points of the interval of integration, t  0andt  1. According to the theory, it holds that u  0u  1 0. Therefore, we approximate the values of the...

Ngày tải lên: 21/06/2014, 20:20