... crucialrole. In this study, we use the Thompson metric introduced by Thomp son [5] for thestudy of solutions to systemsofnonlinear matrix equations involving contractivemappings.We first ... 2011:89http://www.fixedpointtheoryandapplications.com/content/2011/1/89Page 2 of 10 RESEARC H Open AccessSolving systemsofnonlinear matrix equations involving Lipshitzian mappingsMaher Berzig*and Bessem Samet* Correspondence: maher.berzig@gmail.comUniversité ... Hussein-Tunis, B.P. 56, 1008Bab Menara, TunisiaAbstract In this study, both theoretical results and numerical methods are derived for solvingdifferent classes ofsystemsofnonlinear matrix equations...
... analytically continue any solution Y(ζ) of (5.1) or (5.2) along aclosed path γ in C avoiding the singular points {xk} then the columns of Ywill change into their linear combinations: Y →YMγ. ... such systemsof 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 probabilistic models in question ... periodic matrix P , which contains all integrals of motion in the case of difference equations, gives only the monodromy information at in nity anddoes not carry any information about local monodromies...
... of linear Volterra integro-differential equations, ” Mathematical Models & Methods in Applied Sciences, vol. 18, no. 1, pp. 21–45, 2008.2 L. Pandolfi, “Riesz systems and controllability of ... the boundedness of St.Therefore,ft: Stx 2.38is bounded and uniformly continuous on 0, ∞. In addition, the half-line spectrum set of ftis just the following set:iη ∈ ... result willbe obtained by a different point of view.Example 3.1. We reconsider Example 2.1.First,wenotethatα β 0. 3.1 Advances in Difference Equations 7then by 2.21 we obtainx α β...
... that the fixed points 0, ±√α2 are not attracting, since every solutionstarting on the line x 0 is 2-periodic.Remark 4.8. It is interesting to notice that, in the three cases in which there ... β2x0/y0.Our main goal will be to give a description of the dynamics of the system in terms of the eigenvalues of the associated matrix A given in 2.2. We begin with the f ollowing resultconcerning 2-periodic ... nonnegative.2. Preliminaries and First Results Systems of linear fractional difference equations Xn1 FXn in which denominators arecommon for all the components of F have been studied in 8. If...
... supported by the NSF of China, the NSF of Jiangxi Province of China 2008GQS0057, the Youth Foundation of Jiangxi ProvincialEducation Department GJJ09456, and the Youth Foundation of Jiangxi Normal ... of PeriodicSolutions for a Class ofNonlinearEquations withp-Laplacian-Like OperatorsHui-Sheng Ding, Guo-Rong Ye, and Wei LongCollege of Mathematics and Information Science, Jiangxi Normal ... unrestricted use, distribution, andreproduction in any medium, provided the original work is properly cited.We investigate the following nonlinearequations with p-Laplacian-like operators ϕxtfxtxtgxt...
... for Systemsof Nonlinear Second-Order Differential Equations on In niteIntervals in Banach SpacesXingqiu ZhangSchool of Mathematics, Liaocheng University, Liaocheng, Shandong 252059, ChinaCorrespondence ... recently, by using Shauder fixed point theorem, Guo 15 obtained the existence of positive solutions for a class of nth-order nonlinear impulsive singular integro-differential equations in a Banach ... Deimling, Ordinary Differential Equationsin Banach Spaces, vol. 596 of Lecture Notes in Mathematics,Springer, Berlin, Germany, 1977.3 V. Lakshmikantham and S. Leela, Nonlinear Differential Equations...
... Zhou and Y. Xu, “Positive solutions of three- point boundary value problems for systems of nonlinear second order ordinary differential equations, ” Journal of Mathematical Analysis andApplications, ... problems,” Nonlinear Analysis: Theory, Methods & Applications, vol. 42, no. 6, pp. 1003–1010, 2000.[23] H. Wang, “On the number of positive solutions ofnonlinear systems, ” Journal of MathematicalAnalysis ... vol. 46, no. 1, pp. 75–86, 2003.[19] G. Infante and J. R. L. Webb, “Loss of positiv i ty in a nonlinear scalar heat equation,” Nonlinear Differential Equations and Applications, vol. 13, no....
... Andrzej SzulkinWe discuss on the generalized Ulam-Hyers stability for functional equationsin a single variable,including the nonlinear functional equations, the linear functional equations, ... suggestions in improving this paper.References1 D. H. Hyers, “On the stability of the linear functional equation,” Proceedings of the National Academy of Sciences of the United States of America, ... in any medium, provided the original work is properly cited.1. Introduction and preliminariesThe study of functional equations stability originated from a question of Ulam 1940 concern-ing...
... below).For information about publishing your research in Advances in Difference Equations go tohttp://www.advancesindifferenceequations.com/authors/instructions/For information about other SpringerOpen ... mh@yahoo.com; esam mh@almos.vein.huAbstract In this article, we investigate the boundedness property of the solutions of linear and nonlinear discrete Volterra equations in both convolution and non-convolution ... perturbation. In most of our references linear and perturbed linear equations are investigated, moreover the boundedness and estimation of the solutions are founded by usingthe resolvent of the equations. This...
... equation, while in the second example, we will obtain thebound of the solutions of an integral equation.For the sake of proving the global existence of solutions of differential equations, wefirst ... validity of the present integral inequalities.2 Main results In the rest of the paper we denote the set of real numbers as R,andR+=[0,∞)isasubset of R. Dom(f)andIm(f) denote the definition domain ... article as: Zheng and Feng: Some new nonlinear integral inequalities and their applications in thequalitative analysis of differential equations. Journal of Inequalities and Applications 2011...