solution of second order differential equation with variable coefficient

... 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 ... Dosly The spectrum containment of almost periodic solution of second- order neutral delay differential equations with piecewise constant of argument EPCA, for short of the form xtpxt − 1   qx2t ... which guarantees the uniqueness of solution of 1.1 and cannot be omitted. To study the spectrum of almost periodic solution of 1.1, we firstly study the solution of 1.1.Let f 1 n   n1 n  s n f  σ  dσ...

Ngày tải lên: 21/06/2014, 20:20

... 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

... “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 ... problem,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006. 12 Y. Sun, “Positive solutions of singular third -order three-point boundary value problem,” Journal of Mathematical ... 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...

Ngày tải lên: 21/06/2014, 05:20

... conditions for regular or slow variation of all positive solutions of a second- order linear difference equation with arbitrary sign coefficient are established. Relations with the so-called M-classification ... and recessive solutions. Let Advances in Difference Equations 13 R denote the set of all positive recessive solutions of 1.1 and D denote the set of all positive dominant solutions of 1.1.FromTheorem ... Corporation Advances in Difference Equations Volume 2010, Article ID 673761, 16 pages doi:10.1155/2010/673761 Research Article Regularly Varying Solutions of Second- Order Difference Equations with Arbitrary Sign...

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... 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 equation ... studied existence of minimal and maximal quasisolutions of a second- order nonlinear periodic boundary value problem 3,Section4. In 2005, Wang and Shi 4 considered 1.1 with the periodic ... Corporation Advances in Difference Equations Volume 2009, Article ID 347291, 18 pages doi:10.1155/2009/347291 Research Article Inequalities among Eigenvalues of Second- Order Difference Equations with General Coupled...

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Ngày tải lên: 13/08/2014, 16:20

... Difference Equations 13 6. Conclusions In this paper, by using the fixed point theorem of cone, we have investigated the existence of positive solutions for a class of nonlinear fractional differential equations ... positive solution x with r ≤x≤R. The proof is complete. 5. Discussion In this section, we offer some interesting discussion associated with boundary value problems 1.5. Since the proof of the ... preliminaries for discussing the existence of positive solutions of boundary value problem 1.5. Advances in Difference Equations 5 Therefore, the unique solution of BVP 2.1 is x  t   − 1 Γ  α   t 0  t...

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... W. Ge, “Existence of solutions of boundary value problems with integral boundary conditions for second- order impulsive integro-differential equations in Banach spaces,” Journal of Computational ... Article Positive Solutions of nth -Order Nonlinear Impulsive Differential Equation with Nonlocal Boundary Conditions Meiqiang Feng, 1 Xuemei Zhang, 2 and Xiaozhong Yang 2 1 School of Science, Beijing ... introduction of the basic theory of impulsive differential equations, see Lakshmikantham et al. 1; for an overview of existing results and of recent research areas of impulsive differential equations,...

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Ngày tải lên: 22/06/2014, 19:20

... 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 ... 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 Tang and Xin-Ge ... 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...

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... negative. There do not e xist eventua lly positive non-oscillatory solutions of Equation (1.1). Proof. Consider a solution of Equation (1.1) with x −1 , x 0 ∈ ( 0, 1 ). We then know from Lemma 2.3 (A) ... 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 ... A positive semicycle of a solution {x n } ∞ n =− 1 of Equation (1.1) consists of astringofterms{x r , x r+1 , , x m }, all greater than or equal to the equilibrium ¯ x , with r ≥ -1 and m ≤∞such...

Ngày tải lên: 20/06/2014, 22:20

... neutral differential equation, variable delays 1 Introduction The objective of this article is to investigate the stability of the zero solution of the first -order linear neutral differential equations ... results on stability of the zero solution of Equation 1. Then, we generalized the results of the stability to Equation 2. Consider the first -order delay neutral differential equation of the form x  (t ... neutral differential equations with variable delays. Proc Am Math Soc. 136, 909–918 (2008) 19. Ardjouni, A, Djoudi, A: Fixed points and stability in linear neutral differential equations with variable...

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... 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: ... number of positive roots of the function in (2.6), and W be the number of sign changes in its coefficients. Because the radius of convergence of this series is ∞, then by Descartes’ rule of signs...

Ngày tải lên: 21/06/2014, 02:20

... non-linear differential equations of fractional order. Nonlinear Anal 2011, 74:792-804. 34. Zhang L, Wang G: Existence of solutions for nonlinear fractional differential equations with impulses ... nonlinear ordinary differential equations with advanced arguments. Nonlinear Anal 2003, 53:495-505. 40. Yan JR: Oscillation of first -order impulsive differential equations with advanced argument. ... Positive solutions of the three-point boundary value problem for second order differential equations with an advanced argument. Nonlinear Anal 2006, 65:2013-2023. 42. Jankowski T: Positive solutions...

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... and E. Mboumi, “Positive solutions of a boundary value problem for a nonlinear fractional differential equation, ” Electronic Journal of Qualitative Theory of Differential Equations, vol. 2008, no. ... “Positive solutions for boundary-value problems of nonlinear fractional differential equations,” Electronic Journal of Differential Equations, vol. 2006, pp. 1–12, 2006. 21 S. Zhang, “The existence of ... paper investigates the existence and multiplicity of positive solutions for a class of higher- order nonlinear fractional differential equations with integral boundary conditions. The results are...

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... pages doi:10.1155/2009/685040 Research Article Existence of Positive Solution to Second- Order Three-Point BVPs on Time Scales Jian-Ping Sun Department of Applied Mathematics, Lanzhou University of Technology, Lanzhou, Gansu ... on time scales,” Journal of Difference Equations and Applications, vol. 14, no. 7, pp. 723–736, 2008. 9 H. Luo and Q. Ma, “Positive solutions to a generalized second- order three-point boundary-value problem ... scale,” Electronic Journal of Differential Equations, vol. 2003, no. 82, 11 pages, 2003. 8 R. A. Khan, J. J. Nieto, and V. Otero-Espinar, “Existence and approximation of solution of three-point boundary...

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... Article Limit Properties of Solutions of Singular Second- Order Differential Equations Irena Rach ˚ unkov ´ a, 1 Svatoslav Stan ek, 1 Ewa Weinm ă uller, 2 and Michael Zenz 2 1 Department of Mathematical ... formulate sufficient conditions for the existence of at least one solution of problem 5.1a and 5.1b with a>0. In the proof of this theorem, we work also with auxiliary two-point boundary conditions: u  0   ... 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 for periodic problems. The rest of...

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