applications of second order differential equations in engineering
báo cáo hóa học:" Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations" doc
... discontinuous for certain values of the time variable t ∈ 0,T.Thisformoff is motivated by a variety of initial and boundaryvalue problems known from applications and having nonlinear, discontinuous ... Applications Results derived in Theorems 4.1 and 4.2 constitute a useful tool when investigating thesolvability of nonlinear singular equations subject to different types of boundary conditions. In this section, ... analysis of more involved nonlinearities, wheretypically, f has singular points also in u and u. Many applications, compare 2–12, showingthese structural difficulties are our main motivation...
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báo cáo hóa học:" Research Article Homoclinic Solutions of Singular Nonautonomous Second-Order Differential Equations" doc
... “Singular nonlinear problem for ordinary differential equation of the second- order on the half-line,” in Mathematical Models in Engineering, Biology and Medicine:International Conference on Boundary ... Koch, P. Koer, and E. B. Weinmăuller, Initial value problems for systems of ordinary first and second order differential equations with a singularity of the first kind,” Analysis, vol. 21, no. ... ArticleHomoclinic Solutions of Singular Nonautonomous Second- Order Differential Equations Irena Rach˚unkov´aandJanTomeˇcekDepartment of Mathematical Analysis and Applications of Mathematics,...
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Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
... 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...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... 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...
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Báo cáo hóa học: " Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions" pptx
... vol. 8 of Mathematics in Science and Engineering, Academic Press, New York, NY, USA, 1964.2 Y. Shi and S. Chen, “Spectral theory of second- order vector difference equations, ” Journal of Mathematical ... Section 2 gives some preliminaries includingexistence and numbers of eigenvalues of the coupled boundary value problems, and someproperties of eigenvalues of a kind of separated boundary value ... discussions in the first paragraph of Section 2, ϕN−1λ is a polynomial of degree N − 2in , ϕNλ is a polynomial of degree N − 1in , ψN−1λ is a polynomial of degree N − 1in ,andψNλ...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
... of second- order linear equations on timescales. We first establish Picone identity on time scales and obtain our main result by using it.Also, our result unifies the existing ones of second- order ... 1999. Advances in Difference Equations 53. Main Results In this section, we give and prove the main results of this paper.First, we will show that the following second- order linear equation:xΔΔt ... theorem of second- order differential equations see Section 1.Remark 3.6. In the discrete case: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations...
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Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
... 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...
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quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order
... SCHULENBERGERLibrary of Congress Cataloging in Publication Datalvanov, A. V.Quasilinear degenerate and nonuniformly elliptic and parabolic equations of second 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...
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Báo cáo hóa học: " Solvability of boundary value problems with Riemann-Stieltjes Δ-integral conditions for second-order dynamic equations on time scales at resonance" pptx
... 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 in order to unify the theory of continu-ous and discrete calculus. The field of...
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Báo cáo hóa học: " Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument" ppt
... inte-ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto[2-13] and the references therein.Fractional differential equations 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 differential equations 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...
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báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... 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 equations in the first case. For the second case, we leave it to the second part of this paper: Error...
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báo cáo hóa học:" Research Article Exponential Stability of Two Coupled Second-Order Evolution Equations" pptx
... 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...
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báo cáo hóa học:" Research Article Solutions and Green’s Functions for Boundary Value Problems of Second-Order Four-Point Functional Difference Equations" ppt
... Methods of N onlinear Ordinary Differential Equations ,Shandong Science and Technology Press, Jinan, China, 1995. Boundary Value Problems 3 In this paper, we consider the following second- order ... 1.4.4Then solving the BVP 4.1 is equivalent to finding fixed points in K. Obviously Φ iscompletely continuous and keeps the K invariant for λ ≥ 0.Definef0 lim infφτ→ 0mint∈1,Tft, ... functionaldifferential equations, ” Chinese Annals of Mathematics, vol. 23A, no. 6, pp. 1–10, 2001 Chinese.2 Y. Guo and J. Tian, “Two positive solutions for second- order quasilinear differential...
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báo cáo hóa học:" Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval" pot
... 31 .In 31, Guo investigated the minimal nonnegative solution of the followinginitial value problem for a second order nonlinear impulsive integrodifferential equation of Volterra type on an in nite ... area of investigation in the recent years and is much richer than thecorresponding theory of differential equations. For an introduction of the basic theory of impulsive differential equations in ... value problems for second- order nonlinear impulsive differential equations on an in nite interval with an in nite number of impulsive times. All the existingresults obtained in previous papers...
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báo cáo hóa học:" Research Article Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations" pdf
... second- order nonlinear dynamic equations on timescales,” Electronic Journal of Differential Equations, no. 145, pp. 1–8, 2006.17 Q. Kong, “Interval criteria for oscillation of second- order linear ... 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 withmixed nonlinearities,” Advances in Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009.8 D. R. Anderson, “Oscillation of second- order...
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