solution of second order differential equation by runge kutta method

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Ngày tải lên: 13/08/2014, 16:20

... “Existence of solutions for a class of third -order nonlinear boundary value problems,” Journal of Mathematical Analysis and Applications, vol. 294, no. 1, pp. 104–112, 2004. 14 D. Guo, Semi-Ordered Method ... existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory. Motivated by the above works, we consider the singular third -order three-point ... singular boundary value problem of third -order differential equations,” Mathematica Slovaca, vol. 60, no. 4, pp. 485–494, 2010. 4 Y. Sun, “Positive solutions for third -order three-point nonhomogeneous...

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... Difference Equations 2011, 2011:56 http://www.advancesindifferenceequations.com/content/2011/1/56 Page 8 of 8 RESEARC H Open Access Positive periodic solution of higher -order functional difference equation Mei-Lan ... Most of these discrete mathematical models are first -order functional difference equations. Rela- tively, few articles focused on the existence of positive periodic solutions of higher -order functional ... k, , m ẻ N where N denotes the set of positive integers. The purpose of this article is to consider the existence of positive periodic solution of higher -order functional differen ce equatio...

Ngày tải lên: 20/06/2014, 22:20

... <1. The proof of theorem 3 .8 is similar to that of theorem 3.6 by virtue of theorem 2.4, theorem 3.5, Lemma (3.3) and Equation (1.1). Theorem 3.9. The positive equilibrium point of Equation (1.1) ... 2011:46 http://www.advancesindifferenceequations.com/content/2011/1/46 Page 8 of 9 and either m = ∞ or m < ∞ and x m +1 < ¯ x . A negative semicycle of a solution { x n } ∞ n =− 1 of Equation (1.1) consists of a string of terms ... the solution is a nontrivial solution, then we can further divide the solution into two cases: non-oscillatory solution and oscillatory solution. A nontrivial solution {x n } ∞ n =− 1 of Equation...

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... of L 0 which are less than g k λ k ∼−h √ γ k . (2:9) Now, find the asymptotic of those solutions of Equation 2.3 which are greater than g k , i.e., the real roots of Equation 2.5. By virtue of ... equicontinuity of E R , and it comp letes the proof of the discreteness of the spectrum of L 0 . 2 The derivation of the asymptotic formula for eigenvalue distribution of L 0 Suppose that the eigenvalues of ... 2011:7 http://www.boundaryvalueproblems.com/content/2011/1/7 Page 4 of 22 RESEARC H Open Access Study of the asymptotic eigenvalue distribution and trace formula of a second order operator- differential equation Nigar Mahar Aslanova 1,2 Correspondence:...

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Ngày tải lên: 23/06/2014, 00:20

... local estimates of the gradients of solutions of equations of the form (1) by combining the use of certain methods characteristic of the technique of global barriers with constructions applied by Ladyzhenskaya ... study of properties of generalized solutions of quasilin- ear, weakly degenerate parabolic equations. From the results obtained it is evident how the properties of generalized solutions of the equation ... conditions following from (1.7.1). The class of equations determined by conditions (1.8.1) contains as special cases some classes of equations of the type of equations of surfaces with prescribed mean curvature...

Ngày tải lên: 31/05/2014, 01:37

... 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 He (hexiaofei525@sina.com) ISSN ... for a class of even -order differential equations Qi-Ming Zhang ∗1 and Xiaofei He 2 1 College of Science, Hunan University of Technology, Zhuzhou, Hunan 412000, P.R. China 2 College of Mathematics ... (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...

Ngày tải lên: 20/06/2014, 21:20

... W\B r 2 (0 ) ,where B r 2 (0 ) is an open ball in W of radius r 2 centered at 0. Proof. The proof of Proposition 3.2 is the same as the proof of the condition (A2) in the proof of Theorem 3.1. We have proved the ... . proof of Theorem 3.1, system (1.1) has infinite solutions {u k }in W 1,p ( t ) T for ever y posi- tive integer k such that ||u k || đ +,ask đ ∞.TheproofofTheorem3.2is complete. Proof of Theorem ... multiplicity of solutions for p(x)-Laplacian equations in ℝ N . Nonlinear Anal. 59, 173–188 (2004) 19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations....

Ngày tải lên: 20/06/2014, 22:20

... result of boundedness of solutions in the superlinear case i.e., gx, t/x →∞as |x|→∞ was due to Morris 2. By means of KAM theorem, Morris proved that every solution of the differential equation ... assumptions on the parities of Fx, t and ex, t,bya small twist theorem of reversible mapping we obtain the existence of quasiperiodic solutions and boundedness of all the solutions. 1. Introduction ... ϕx and et, by using a variant of Moser’s small twist theorem 9 to the Pioncar ´ e map, the author obtained the existence of quasi-periodic solutions and the boundedness of all solutions. Then...

Ngày tải lên: 21/06/2014, 07:20

... l  j       3.11 are finite. Equation 3.10 is a inhomogeneous second- order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions ... 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 ... constant. Equation 4.14 is an inhomogeneous second- order linear difference equation; its solution takes the form of a particular solution added to an arbitrary linear combination of solutions...

Ngày tải lên: 21/06/2014, 11:20

... ∪NRV 2 . Proof . First we show the last part of the statement. Let {x, y}be a fundamental set of solutions of 1.1,withy ∈NRV 1 , x ∈NRV 2 ,andletz be an arbitrary solution of 1.1,with z k > ... possible values of the limits of y and of Δy. Solutions in M  ∞,B , M  ∞,0 , M  B,0 are sometimes called, respectively, dominant solutions, intermediate solutions, and subdominant solutions, since, ... positive solutions is particularly meaningful in the study of dominant and recessive solutions. Let Advances in Difference Equations 13 R denote the set of all positive recessive solutions of 1.1...

Ngày tải lên: 21/06/2014, 11:20

... a unique solution and then studied the dependence of this solution on the parameters λ and μ.Sun11 discussed the existence and nonexistence of positive solutions to a class of third -order three-point ... II,” Journal of Mathematical Analysis and Applications, vol. 330, no. 2, pp. 1393–1411, 2007. 10 L. Kong and Q. Kong, “Uniqueness and parameter dependence of solutions of second- order boundary ... which is the unique positive solution of the BVP 1.5–1.7. The first part of the theorem is proved. In the rest of the proof, we will prove that such a positive solution u λ t satisfies properties...

Ngày tải lên: 21/06/2014, 11:20

... results of existence and multiplicity of positive solutions to the BVP 1.3 by using lower and upper solutions technique. Motivated by the above works, we will study the existence results of unbounded positive ... “Positive solutions of operator equations on half-line,” Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 423–435, 2006. 23 Y. Wang, L. Liu, and Y. Wu, “Positive solutions of ... 2001. 21 C. Bai and J. Fang, “On positive solutions of boundary value problems for second- order functional differential equations on infinite intervals,” Journal of Mathematical Analysis and Applications,...

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... pages doi:10.1155/2010/973731 Research Article Solutions 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 ... existence of positive solutions for a second- order functional difference equation with four-point boundary conditions. 1. Introduction In recent years, boundary value problems BVPs of differential ... holds. Then the second- order four-point BVP 2.13 has a unique solution which is given in 2.29. Proof. We need only to show the uniqueness. Obviously, wt in 2.29 is a solution of BVP 2.13....

Ngày tải lên: 21/06/2014, 11:20