applications of second order differential equations to real world systems

... Article Limit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach ˚ unkov ´ a, 1 Svatoslav Stan ˇ ek, 1 Ewa Weinm ¨ uller, 2 and Michael Zenz 2 1 Department of Mathematical ... useful tool when investigating the solvability 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 ... h tending to zero, or equivalently, grids becoming finer. We finally observe experimentally the order of convergence of the numerical method collocation. Clearly, we do not expect very hight order to...

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 21/06/2014, 20:20

... contributed to these interesting 2 Lyapunov-type inequalities for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, ... on [α, β], too. Then, by a similar method 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.com Journal...

Ngày tải lên: 20/06/2014, 21:20

... sequences and second order difference equations, ” Journal of Difference Equations and Applications, vol. 14, no. 1, pp. 17–30, 2008. 7 J. Jaro ˇ s and T. Kusano, “Self-adjoint differential equations ... properties of Emden-Fowler difference equations, ” Central European Journal of Mathematics , vol. 7, no. 2, pp. 322–334, 2009. 13 P. ˇ Reh ´ ak, “Oscillatory properties of second order half-linear ... eventually of one sign. In this case, all nonoscillatory 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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... 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 antiperiodic boundary conditions,” Journal of Mathematical Analysis and Applications, ... 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...

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... 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: μt ≡ 1. This result is the same as Sturm comparison theorem of second- order difference equations...

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... Spectrum of Almost Periodic Solution of Second- Order Neutral Delay Differential Equations with Piecewise Constant of Argument Li Wang and Chuanyi Zhang Department 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 with piecewise...

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... devoted to questions of solvability of basic boundary value problems for quasilinear degenerate and nonuniformly elliptic and parabolic equations of second order, and also 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 quasilinear elliptic equations of the form (1)is the question of distinguishing classes of equations for...

Ngày tải lên: 31/05/2014, 01:37

... 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 9 One might be tempted to follow the standard ideas with lower and upper solutions 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 the survey of Hartung et al. [8] and references therein. As main improvements in this article with regard to previous...

Ngày tải lên: 20/06/2014, 20:20

... 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 ... 2011:42 http://www.advancesindifferenceequations.com/content/2011/1/42 Page 7 of 18 RESEARC H Open Access Solvability of boundary value problems with Riemann-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 the sufficient conditions for the existence of at least one solution to problem (1.1). Theorem...

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... 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 and multiplicity of solutions (or positive solutions) of three-point BVPs for nonlinear inte- ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto [2-13] and the references...

Ngày tải lên: 21/06/2014, 03:20

... Asymptotic Solutions of Second- order Linear Difference Equation II: the second case. In the rest of this paper, we would like to give an example to show how to use the results 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 is similar to that of Olver to obtain error bounds to the Liouville-Green WKB asymptotic expansion of solutions to second- order differential equations. It should be pointed...

Ngày tải lên: 21/06/2014, 11:20

... is give to illustrate that the result obtained can be applied to concrete partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution ... Article Exponential Stability of Two Coupled Second- Order Evolution Equations Qian Wan and Ti-Jun Xiao Shanghai 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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... may transform our existence problem of positive solutions of BVP 3.1 into a fixed point problem of operator 3.13. Lemma 3.3. Consider that ΦK ⊂ K. Proof. If t ∈ −τ, 0 and t  T 1, ΦytαΦη ... and Green’s Functions for Boundary Value Problems of Second- Order Four-Point Functional Difference Equations Yang Shujie and Shi Bao Institute of Systems Science and Mathematics, Naval Aeronautical ... theory, Deng and Shi 5 studied the existence and multiplicity of the boundary value problems to a class of second- order functional difference equations Lu n  f  n, u n1 ,u n ,u n−1  1.1 with boundary...

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... oscillation criteria were recently extended to second- order dynamic equations in 6–10. Further results on 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 with oscillatory ... Difference Equations, vol. 2009, Article ID 938706, 20 pages, 2009. 8 D. R. Anderson, “Oscillation of second- order forced functional dynamic equations with oscillatory potentials,” Journal of Difference...

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