applications of second order differential equations to real world systems
báo cáo hóa học:" Research Article Limit Properties of Solutions of Singular Second-Order Differential Equations" doc
... ArticleLimit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach˚unkov´a,1Svatoslav Stanˇek,1Ewa Weinm¨uller,2and Michael Zenz21Department of Mathematical ... useful tool when investigating thesolvability 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 ... htending to zero, or equivalently, grids becoming finer.We finally observe experimentally the order of convergence of the numerical methodcollocation. Clearly, we do not expect very hight order to...
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Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
... contributed to these interesting2Lyapunov-type inequalities for a class of even -order differential equations Qi-Ming Zhang∗1and Xiaofei He21College of Science, Hunan University of Technology, ... on [α, β], too. Then, by a similarmethod to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately.For the other ordinary cases, i.e., a = 0, we only need to move the ... in Journal of Inequalities and Applications go to http://www.journalofinequalitiesandapplications.com/authors/instructions/For information about other SpringerOpen publications go to http://www.springeropen.comJournal...
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báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... sequences and second order difference equations, ”Journal of Difference Equations and Applications, vol. 14, no. 1, pp. 17–30, 2008.7 J. Jaroˇs and T. Kusano, “Self-adjoint differential equations ... properties of Emden-Fowlerdifference equations, ” Central European Journal of Mathematics, vol. 7, no. 2, pp. 322–334, 2009.13 P.ˇReh´ak, “Oscillatory properties of second order half-linear ... eventually of one sign. In this case, allnonoscillatory solutions of 1.1 are eventually monotone, together with their first difference,and therefore can be a priori classified according to their monotonicity...
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Báo cáo hóa học: " Research Article Inequalities among Eigenvalues of Second-Order Difference Equations with General Coupled Boundary Conditions" pptx
... problems for second- order difference equations. Existence of eigenvalues is proved, numbers of their eigenvalues are calculated,and their relationships between the eigenvalues of second- order difference ... Difference Equations 4 Y. Wang and Y. Shi, “Eigenvalues of second- order difference equations with periodic and antiperiodicboundary conditions,” Journal of Mathematical Analysis and Applications, ... vol. 8 of Mathematics in Science andEngineering, Academic Press, New York, NY, USA, 1964.2 Y. Shi and S. Chen, “Spectral theory of second- order vector difference equations, ” Journal of Mathematical...
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Báo cáo hóa học: " Research Article Sturm-Picone Comparison Theorem of Second-Order Linear Equations on Time Scales" ppt
... equations of second order, ” Annals of Mathematics, vol. 65, pp. 197–202, 1957.6 R. Zhuang, “Sturm comparison theorem of solution for second order nonlinear differential equations, ” Annals of ... differential equations of second order, ” Proceedings of the American Mathematical Society, vol. 13, pp. 603–610, 1962.4 W. Leighton, “Some elementary Sturm theory,” Journal of Differential Equations, ... 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 ... “Corrigendum to: “On the spectrum of almost periodic solution of second order scalar functional differential equations with piecewise constant argument”,” Journal of Mathematical Analysis and Applications, ... 0,which leads to a 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...
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quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order
... devoted to questions of solvability of basic boundary value problemsfor quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, andalso to the investigation of differential ... when itis necessary to refer to a formula of another chapter. For example, in Chapter 7 the notation (5.1.2) is used to refer to formula (1.2) of Chapter 5. Reference to numbers of theorems and sections ... with this, one of the first questions of the general theory of boundary value problems for quasilinearelliptic equations of the form (1)is the question of distinguishing classes of equations for...
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Báo cáo toán học: " Minimal and maximal solutions to first-order differential equations with state-dependent deviated arguments" pptx
... seems to be a peculiar feature of equa-tions with deviated arguments, see [1] for an example with a second- order equation. Therefore, we are obliged to distinguish between the concepts of minimal ... in the sense of Definition 1.Title Suppressed Due to Excessive Length 9One might be tempted to follow the standard ideas with lower and uppersolutions to define a lower solution of (1) as some ... kind of prob-lems. For the qualitative study of this type of problems we can cite thesurvey of Hartung et al. [8] and references therein.As main improvements in this article with regard to previous...
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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
... time scales in order to unify the theory of continu-ous and discrete calculus. The field of dynamical equations on time scales contains,links and extends the classical theory of differential ... 2011:42http://www.advancesindifferenceequations.com/content/2011/1/42Page 7 of 18RESEARC H Open AccessSolvability of boundary value problems withRiemann-Stieltjes Δ-integral conditions for second- order dynamic equations ... continuous. The proof is completed.Now, we are ready to apply the coincidence degree t heorem of Mawhin to give thesufficient conditions for the existence of at least one solution to problem (1.1).Theorem...
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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
... theory and applications of integer order differential equations wit h deviat ed arguments, we refer the reader to the refer-ences [39-45].As far as we know, fractional order differential equations ... found to be important mathema-tical tools for the better understanding of several real world problems in physics,mechanics, engineering, economics, etc. [37,38]. In fact, the theory of integer order ... existence andmultiplicity of solutions (or positive solutions) of three-point BVPs for nonlinear inte-ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto[2-13] and the references...
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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 DifferenceEquation II: the second case.In the rest of this paper, we would like to give an example to show how to use theresults of this paper to obtain ... 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 ... used in this paper issimilar to that of Olver to obtain error bounds to the Liouville-Green WKB asymptoticexpansion of solutions to second- order differential equations. It should be pointed...
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báo cáo hóa học:" Research Article Exponential Stability of Two Coupled Second-Order Evolution Equations" pptx
... is give to illustrate that the result obtainedcan be applied to concrete partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution ... ArticleExponential Stability of Two Coupled Second- Order Evolution Equations Qian Wan and Ti-Jun XiaoShanghai Key Laboratory for Contemporary Applied Mathematics, School of Mathematical Sciences,Fudan ... properly 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...
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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
... may transform our existence problem of positive solutions of BVP 3.1 into a fixedpoint problem of operator 3.13.Lemma 3.3. Consider that ΦK ⊂ K.Proof. If t ∈ −τ, 0 and t T 1, ΦytαΦη ... and Green’s Functions forBoundary Value Problems of Second- Order Four-Point Functional Difference Equations Yang Shujie and Shi BaoInstitute of Systems Science and Mathematics, Naval Aeronautical ... theory,Deng and Shi 5 studied the existence and multiplicity of the boundary value problems to aclass of second- order functional difference equations Lun fn, un1,un,un−11.1with boundary...
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báo cáo hóa học:" Research Article Oscillation of Second-Order Mixed-Nonlinear Delay Dynamic Equations" pdf
... oscillationcriteria were recently extended to second- order dynamic equations in 6–10. Further resultson oscillatory and nonoscillatory behavior of the second order nonlinear dynamic equations on time scales ... arguments,” to appear in Journal of Difference Equations and Applications .10 A. F. G¨uvenilir and A. Zafer, Second- order oscillation of forced functional differential equations withoscillatory ... Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009.8 D. R. Anderson, “Oscillation of second- order forced functional dynamic equations with oscillatorypotentials,” Journal of Difference...
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