applications of second order differential equations in economics

... discontinuous for certain values of the time variable t ∈ 0,T.Thisformoff is motivated by a variety of initial and boundary value problems known from applications and having nonlinear, discontinuous ... Applications Results derived in Theorems 4.1 and 4.2 constitute a useful tool when investigating the solvability of nonlinear singular equations subject to different types of boundary conditions. In this section, ... analysis of more involved nonlinearities, where typically, f has singular points also in u and u  . Many applications, compare 2–12, showing these structural difficulties are our main motivation...

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... “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. Weinm ă uller, Initial value problems for systems of ordinary first and second order differential equations with a singularity of the first kind,” Analysis, vol. 21, no. ... Article Homoclinic Solutions of Singular Nonautonomous Second- Order Differential Equations Irena Rach ˚ unkov ´ aandJanTome ˇ cek Department of Mathematical Analysis and Applications of Mathematics,...

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... 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-2012-5 Qi-Ming Zhang (zhqm20082008@sina.com) Xiaofei ... below). For information about publishing your research in Journal of Inequalities and Applications go to http://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 can obtain the...

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... k ≥ a In this case, completely analyzed in 1, any positive solution y is either decreasing or eventually 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 regularly varying with two different indices in case ... solutions of 1.1 and D denote the set of all positive 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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... 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 including existence and numbers of eigenvalues of the coupled boundary value problems, and some properties of eigenvalues of a kind of separated boundary value ... discussions in the first paragraph of Section 2, ϕ N−1 λ is a polynomial of degree N − 2in , ϕ N λ is a polynomial of degree N − 1in , ψ N−1 λ is a polynomial of degree N − 1in ,andψ N λ...

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... of second- order linear equations on time scales. 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 5 3. 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: x ΔΔ  t   ... 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 ... ω. This brings more convenience to study the spectrum containment of almost periodic solution of 1.1. Now, we are in the position to show the Main Theorem. The proof of Main Theorem Since H 1  ... periodic. In this paper, we investigate the existence, uniqueness, and spectrum containment of almost periodic solutions of 1.1. T he main result obtained in this paper is different from that given in...

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... SCHULENBERGER Library of Congress Cataloging in Publication Data lvanov, 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 admissible structure of linear elliptic equations is determined mainly by the condition of sufficient smoothness of the coefficients, in ... priori estimate 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 and maxalul. The estimates of maxaulvul...

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... yklie@ynu.edu. cn Department of Mathematics, Yunnan University Kunming, Yunnan 650091, People’s Republic of China Abstract In this paper, by making use of the coincidence degree theory of Mawhin, the existence of the ... problems do in the continuous case. For instance, in BVPs (1.1), let g(s)= k i=1 a i (s t i ), where k 1isaninteger,a i ẻ [0, ∞), i = 1, , k, {t i } k i=1 is a finite increasing sequence of distinct ... Δ?Δ?-integral conditions, resonance, time scales 1 Introduction Hilger [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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... inte- ger -order ordinary differential equations. Toidentifyafew,wereferthereaderto [2-13] and the references therein. Fractional differential equations arise in many engineering and scientific disciplines as ... 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, Cone 1 Introduction The study of three-point BVPs for nonlinear integer -order ordinary...

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... asymptotic solutions of second- order linear differential equations, the method used in Wong and Li’s papers cannot give us way to 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 is positive. 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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... partial differential equations. 1. Introduction Of concern is the exponential stability of two coupled second- order evolution equations one is an integro-differential equation in Hilbert space H u   t   ... and reproduction 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 ... β 2   a   T S    √ Aut    2 dt   T S    √ Avtβut    2 dt. 2.28 Proof. Taking the inner product of both sides of 1.2 with vt and integrating over S, T , we see  T S   v  t   2 dt   T S  v   t  ,v  t    dt...

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... 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. 4.4 Then solving the BVP 4.1 is equivalent to finding fixed points in K. Obviously Φ is completely continuous and keeps the K invariant for λ ≥ 0. Define f 0  lim inf φ τ → 0 min t∈1,T f  t, ... functional differential 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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... 31 .In 31, Guo investigated the minimal nonnegative solution of the following initial 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 the corresponding 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 existing results obtained in previous papers...

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... second- order nonlinear dynamic equations on time scales,” 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 with mixed 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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