power series solution of differential equations ppt

... Advances in Difference Equations 2011, 2011:58 http://www.advancesindifferenceequations.com/content/2011/1/58 Page 3 of 12 RESEARCH Open Access Polynomial solutions of differential equations H Azad * , ... polynomial solutions of a class of linear differential equations of the second order. Bull A M S. 36, 77–84 (1930). doi:10.1090/S0002-9904-1930-04888-0 Azad et al. Advances in Difference Equations ... Correspondence: hassanaz@kfupm.edu.sa Department of Mathematics & Statistics, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia Abstract A new approach for investigating polynomial solutions of differential equations...

Ngày tải lên: 20/06/2014, 22:20

... made available soon. Further results of the estimate of growth of entire solutions of some classes of algebraic differential equations Advances in Difference Equations 2012, 2012:6 doi:10.1186/1687-1847-2012-6 Oi ... solutions of some algebraic differential equations and improve the related results of Bergweiler, Barsegian, and others. We also estimate the growth order of entire solutions of a type system of a ... [w (m) (z)] r m , 17 [11] Gu, RM, Ding, JJ, Yuan, WJ: On the estimate of growth order of solutions of a class of systems of algebraic differential equations with higher orders. J. Zhanjiang Normal Univ. (in...

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... 1.34 then 1.30 has one and only one ω-periodic solution. 10 Boundary Value Problems 3. Proof of the main results Proof of Theorem 1.1. Without loss of generality, it can be assumed that h00. ... If the function u is an ω-periodic solution of 1.3, then its restriction to 0,ω is a solution of problem 2.26, 2.27, and vice versa, if u is a solution of problem 2.26, 2.27, then its ... 2.31. Let u be a solution of problem 2.30, 2.27 for some λ ∈0, 1 . Then its periodic extension to R with a period ω is a solution of 2.32, and according to one of the conditions of the lemma, admits...

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... equal to I. The proof of uniqueness is complete. To prove the existence we note, first of all, that it suffices to provide a proof if one of the κ i ’s is equal to ±1 and one of the δ j ’s is equal ... deformations of two types: continuous ones, when x i move in the complex plane and B i = B i (x) form a solution of a sys- tem of partial differential equations called Schlesinger equations, and ... be the solution of the difference Schlesinger equations (3.1)– (3.3) with the initial conditions {B i (0) = B i }, and let B i (x 1 , ,x n )bethe solution of the classical Schlesinger equations...

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... Canonical form of parabolic equations 69 3.5 Canonical form of elliptic equations 70 3.6 Exercises 73 vii 1.4 Differential equations as mathematical models 13 1.4.4 Random motion Random motion of minute ... finding explicit solutions. Be- cause of the immense importance of PDEs in the different branches of physics, every mathematical development that enabled a solution of a new class of PDEs was accompanied ... into a set of far simpler problems, is quite general. 1.7 Exercises 1.1 Show that each of the following equations has a solution of the form u(x, y) = f (ax + by) for a proper choice of constants...

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... 1–10, find the general solution of the differential equation. Chapter 0 Ordinary Differential Equations 3 Principle of Superposition. If u 1 (t) and u 2 (t) are solutions of the same linear homogeneous ... others. Instead of just finding the solution of a boundary value problem, we will be looking for parameter values that permit the existence of solutions of special form. Example: Buckling of a Column. A ... 1. This method of assuming an exponential form for the solution works for linear homogeneous equations of any order with constant coefficients. In all 6 Chapter 0 Ordinary Differential Equations 0...

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... second example, we will obtain the bound of the solutions of an integral equation. For the sake of proving the global existence of solutions of differential equations, we first recall some basic ... integral equation, differential equa- tion, bounded 1 Introduction During the past decades, with the development of the theory of differential and integral equations, a lot of integral inequalities, ... discovered, which play an important role in the research of boundedness, global existence, stability of solutions of differential and integral equations. In [9], the following two theorems for retarded...

Ngày tải lên: 21/06/2014, 01:20

... dealing with the boundedness of solutions of certa in delay dynamic equations on time scales. Feng et al. Journal of Inequalities and Applications 2011, 2011:29 http://www.journalofinequalitiesandapplications.com/content/2011/1/29 Page ... in the theory of dynamics equations. Journal of Inequalities and Applications 2011 2011:29. Feng et al. Journal of Inequalities and Applications 2011, 2011:29 http://www.journalofinequalitiesandapplications.com/content/2011/1/29 Page ... and discrete analysis, and play an important role in the research of boundedness, uniqueness, stabi- lity of solutions of dynamic equations on time scales. But to our knowledge, delay inte- gral...

Ngày tải lên: 21/06/2014, 01:20

... study of boundedness, uniqueness, continuous dependence of solutions of certain difference equations. Feng et al. Advances in Difference Equations 2011, 2011:21 http://www.advancesindifferenceequations.com/content/2011/1/21 Page ... the usefulness of the established results by applying them to study the boundedness, uniqueness, and continuous depen- dence on initial data of solutions of certain difference equations. Throughout ... Difference Equations 2011, 2011:21 http://www.advancesindifferenceequations.com/content/2011/1/21 Page 3 of 17 where  H ,  f ,  w are defined in (21). Then following in a same manner as the proof of...

Ngày tải lên: 21/06/2014, 02:20

... solutions of E. Since every solution of E is also a solution of E C , we are in view of a generalization of Kiguradze’s lemma see 4 or 11 in the following structure of the nonoscillatory solutions ... results is such solution of V  that satisfies 2.2. If we eliminate the solutions of degree 2 of E,we get the studied property P 0  of E. The next theorem and its proof provide the details. Theorem ... the nonoscillatory solutions of E. Lemma 2.5. Assume that vt is a positive solution of V  satisfying 2.2, then every positive solution yt of Eis either of degree 2, that is, y>0, 1 v y  >...

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