... Difference Equations Volume 2010, Article ID 143298, 8 pagesdoi:10.1155/2010/143298Research ArticleOn Connection between Second- Order Delay Differential Equations and Integrodifferential Equations ... obtained by transforming second- order delay dierential equations ăxtat xgt btxht 0 to first -order differential equations. 1. Introduction and PreliminariesThe secondorder delay dierential equationăxt ... Advances in Difference Equations One of the methods used to study 1.1 is transforming the second- order delaydifferential equation to a first -order differential or integrodifferential equations with delay.A...
... solutions to second order linear difference equations in the first case. For the second case, we leave it to the second part of this paper: Error Bound for Asymptotic Solutions of Second- order Linear ... nonlinear first -order difference equation. 2 Advances in Difference Equations Unlike t he method used by Olver 4 to treat asymptotic solutions of second- order linear differential equations, the ... for second- order linear difference equations, ” Journal ofComputational and Applied Mathematics, vol. 41, no. 1-2, pp. 65–94, 1992.3 R. Wong and H. Li, “Asymptotic expansions for second- order...
... pagesdoi:10.1155/2011/212980Research ArticleMultiple Positive Solutions of a SingularEmden-Fowler Type Problem for Second- Order Impulsive Differential SystemsEun Kyoung Lee and Yong-Hoon LeeDepartment of Mathematics, Pusan ... solutions of two-point boundary value problems for systemsof nonlinear second- order singular and impulsive differential equations, ” Nonlinear Analysis: Theory,Methods & Applications, vol. ... the existence, and multiplicity of positive solutions of a singular boundaryvalue problem for second- order differential systems with impulse effects. By using the upper andlower solutions method...
... concentrated on lower -order neutralfunctional differential equations, while studies on higher -order neutral functional differential equations are rather infrequent, especially on higher -order p-Laplacian ... 2, pp. 1161–1173,2007.9 J. Wu and Z. Wang, “Two periodic solutions of second- order neutral functional differential equations, ” Journal of Mathematical Analysis and Applications, vol. 329, no. ... ArticleExistence and Lyapunov Stability ofPeriodic Solutions for Generalized Higher -Order Neutral Differential Equations Jingli Ren,1Wing-Sum Cheung,2and Zhibo Cheng11Department of Mathematics,...
... for secondorder impulsivedifferential equations with advanced arguments,” Applied Mathematics and Computation, vol. 197, no.1, pp. 179–189, 2008.17 T. Jankowski, “Positive solutions to second ... boundary value problem for secondorder nonlinearsingular differential equations, ” Georgian Mathematical Journal, vol. 7, no. 1, pp. 133–154, 2000.22 C. Corduneanu, Integral Equations and Applications, ... 284–302, 1997.12 R. P. Agarwal and D. O’Regan, “Multiple nonnegative solutions for secondorder impulsivedifferential equations, ” Applied Mathematics and Computation, vol. 114, no. 1, pp. 51–59, 2000.13...
... Dynamics of SecondOrder Rational Difference Equations, Chapman &Hall/CRC, Boca Raton, Fla, USA, 2002.2 G. Ladas, “Invariants for generalized Lyness equations, ” Journal of Difference Equations ... Difference Equations Volume 2009, Article ID 128602, 27 pagesdoi:10.1155/2009/128602Research ArticleGlobal Behavior of Solutions to Two Classes of Second- Order Rational Difference Equations Sukanya ... difference equations, ” AppliedMathematics Letters, vol. 13, no. 7, pp. 1–8, 2000.5 A. M. Amleh, E. Camouzis, and G. Ladas, “On second- order rational difference equation—I,” Journalof Difference Equations...
... of solutions of initial-boundary value problems for parabolic equations in domains with conical points,” Journal of Differential Equations, vol. 245, no. 7, pp. 1801–1818, 2008.6 V. A. Solonnikov, ... smoothness of solutions to second initial boundaryvalue problems for Schrăodinger systems in cylinders with non-smooth bases,” Electronic Journal ofDifferential Equations, vol. 2008, no. 35, ... measurable complex functions ux, t that havegeneralized derivatives up to order m with respect to x and up to order l with respect to twith the normuHm,le−γt,Q∞⎛⎝Q∞⎡⎣|α|m|∂αu|2lj1|utj|2⎤⎦e−2γtdx...
... this theorem, we get Ft2 · γ.4. Second- Order Fuzzy Differential Equations In this section, we study the fuzzy initial value problem for a second- order linear fuzzydifferential equation:⎧⎪⎪⎪⎨⎪⎪⎪⎩yt ... twosolutions.5. Higher -Order Fuzzy Differential Equations Selecting different types of derivatives, we get several solutions to fuzzy initial value problemfor second- order fuzzy differential equations. Theorem ... higher -order differentiability for fuzzy functions.Then we interpret Nth -order fuzzy differential equations using this concept. We introduce newdefinitions of solution to fuzzy differential equations. ...
... CorporationAdvances in Difference Equations Volume 2011, Article ID 879649, 14 pagesdoi:10.1155/2011/879649Research ArticleExponential Stability of Two Coupled Second- Order Evolution Equations Qian Wan and ... be applied to concrete partial differential equations. 1. IntroductionOf concern is the exponential stability of two coupled second- order evolution equations oneis an integro-differential equation ... 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 if theconvolution...
... Difference Equations Volume 2009, Article ID 143175, 14 pagesdoi:10.1155/2009/143175Research ArticleOn the Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with ... contradiction. The claim follows. 14 Advances in Difference Equations 12 R. Yuan, “On the spectrum of almost periodic solution of second- order differential equations withpiecewise constant argument,” Nonlinear ... periodic differential equations and almost periodic flows,” Journal ofDifferential Equations, vol. 5, no. 1, pp. 167–181, 1969.18 R. Yuan, “Pseudo-almost periodic solutions of second- order neutral...
... Difference Equations Volume 2009, Article ID 347291, 18 pagesdoi:10.1155/2009/347291Research ArticleInequalities among Eigenvalues of Second- Order Difference Equations withGeneral Coupled Boundary ... γyb δyΔb 0, 2.9 18 Advances in Difference Equations 4 Y. Wang and Y. Shi, “Eigenvalues of second- order difference equations with periodic and antiperiodicboundary conditions,” ... May 2009Recommended by Johnny HendersonThis paper studies general coupled boundary value problems for second- order difference equations. Existence of eigenvalues is proved, numbers of their eigenvalues...
... “Existence of one-signed periodic solutions of some second- order differential equations via a Krasnoselskii fixed point theorem,” Journal of Differential Equations, vol. 190, no. 2, pp. 643–662,2003.38 ... pagesdoi:10.1155/2009/540863Research ArticleRecent Existence Results for Second- Order Singular Periodic Differential Equations Jifeng Chu1, 2and Juan J. Nieto31Department of Mathematics, ... Differential Equations, vol. 103, no. 2, pp. 260–277, 1993.3 J. Chu, X. Lin, D. Jiang, D. O’Regan, and R. P. Agarwal, “Multiplicity of positive periodic solutions to second order differential equations, ”...
... pagesdoi:10.1155/2009/905769Research ArticleLimit Properties of Solutions of Singular Second- OrderDifferential Equations Irena Rach˚unkov´a,1Svatoslav Stanek,1Ewa Weinmăuller,2and ... becoming finer.We finally observe experimentally the order of convergence of the numerical methodcollocation. Clearly, we do not expect very hight order to hold, since the analytical solutionhas ... 5.44-5.1a with a 1.Tab le 1 : Estimated convergence order for the periodic boundary value problem 5.43-5.1a and a 1.i Error estimate Conv. order 1 5.042446e–003 —2 2.850171e–003 0.8230753...
... pagesdoi:10.1155/2009/959636Research ArticleHomoclinic Solutions of Singular Nonautonomous Second- OrderDifferential Equations Irena Rach˚unkov´aandJanTomeˇcekDepartment of Mathematical Analysis ... and second order differential equations with a singularity of the first kind,” Analysis, vol. 21, no. 4, pp.373–389, 2001.7 D. Bonheure, J. M. Gomes, and L. Sanchez, “Positive solutions of a second- order ... Rach˚unkov´aandJ.Tomeˇcek, “Singular nonlinear problem for ordinary differential equation ofthe second- order on the half-line,” in Mathematical Models in Engineering, Biology and Medicine:International...