... soon.Lyapunov-type inequalities for a class of even -order differential equations Journal of Inequalities and Applications 2012, 2012:5 doi:10.1186/1029-242X-2012-5Qi-Ming Zhang (zhqm20082008@sina.com)Xiaofei ... below).For information about publishing your research in Journal of Inequalities and Applications go tohttp://www.journalofinequalitiesandapplications.com/authors/instructions/For information ... (2.11)Since |x(c)| > 0, divided the last inequality of (2.11) by |x(c)|, we can obtain (2.10). By a similar method in the proof of Theorem 1.1, applying Lemmas 2.1 and 2.3, we canobtain the...
... k ≥ a In this case, completely analyzed in 1, any positive solution y is either decreasing oreventually increasing. We say that y is of class M in the first case, of class M− in the second one. ... difference tending to zero, have two possible asymptotic behaviors,since they can be slowly varying or regularly varying with index 1 in case ii, or regularlyvarying with two different indices in case ... solutions of 1.1 and D denote the set of allpositive dominant solutions of 1.1.FromTheorem 4.1, taking into account Theorem 3.1,the following characterization of recessive and dominant solution...
... Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with Piecewise Constant of ArgumentLi Wang and Chuanyi ZhangDepartment of Mathematics, Harbin Institute of ... ω. This brings more convenience to study the spectrumcontainment of almost periodic solution of 1.1. Now, we are in the position to show theMain Theorem.The proof of Main TheoremSince H1 ... periodic. In this paper, we investigate the existence,uniqueness, and spectrum containment of almost periodic solutions of 1.1. T he main resultobtained in this paper is different from that given in...
... SCHULENBERGERLibrary of Congress Cataloging in Publication Datalvanov, A. V.Quasilinear degenerate and nonuniformly elliptic and parabolic equationsofsecond order. (Proceedings of the Steklov Institute of ... satisfying (1.1) in SZ and coinciding with T on 852. While the admissiblestructure of linear elliptic equations is determined mainly by the condition of sufficient smoothness of the coefficients, in ... prioriestimate of maxnivul breaks down into two steps: 1) obtaining maxaalvul in terms of maxsljul, and 2) obtaining an estimate of maxr 1vul in terms of maxanlvul andmaxalul. The estimates of maxaulvul...
... yklie@ynu.edu.cnDepartment of Mathematics,Yunnan University Kunming,Yunnan 650091, People’s Republic of ChinaAbstract In this paper, by making use of the coincidence degree theory of Mawhin, theexistence of the ... problemsdo in the continuous case. For instance, in BVPs (1.1), letg(s)=ki=1ai(s ti),where k 1isaninteger,aiẻ [0, ∞), i = 1, , k,{ti}ki=1is a finite increasingsequence of distinct ... Δ?Δ?-integral conditions,resonance, time scales1 IntroductionHilger [1] introduced the notion of time scales inorder to unify the theory of continu-ous and discrete calculus. The field of...
... inte-ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto[2-13] and the references therein.Fractional differentialequations arise in many engineering and scientific disciplinesas ... accurate than integer- order models, i.e., there are more degrees of freedom in the fractional -order models. In consequence, the subject of fractional differentialequations is gaining much impor-tance ... Three-point boundary value problem, Fractional differ-ential equations, Guo-Krasnoselskii fixed point theorem, Cone1 IntroductionThe study of three-point BVPs for nonlinear integer -order ordinary...
... asymptotic solutions of second- order linear differential equations, the method used in Wong and Li’s papers cannot give us wayto obtain error bounds of these asymptotic solutions. Only order estimations ... two cases of 3, respectively. In the rest of this section, we introduce the main results of 3 in the case that k ispositive. In the next section, we give two lemmas on estimations of bounds ... completed the estimate of the error bounds for asymptotic solutions to second order linear difference equationsin the first case. For the second case, we leave it to the second part of this paper: Error...
... partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution equations oneis an integro-differential equation in Hilbert space Hut ... andreproduction in any medium, provided the original work is properly cited.By using the multiplier technique, we prove that the energy of a system of two coupled second order evolution equations ... β2aTS√Aut2dt TS√Avtβut2dt.2.28Proof. Taking the inner product of both sides of 1.2 with vt and integrating over S, T ,we seeTSvt2dt TSvt,vtdt...