application of second order differential equation in real life

... Reports in Mathematics in Science and Engineering, Academic Press, Boston, Mass, USA, 1988. 16 D. Guo, V. Lakshmikantham, and X. Liu, Nonlinear Integral Equations in Abstract Spaces, vol. 373 of Mathematics ... contraction mapping principle implies that  A n 0 has a unique fixed point x ∗ in CI,andso  A has a unique fixed point x ∗ in CI; by the definition of  A, A has a unique fixed point x ∗ in CI,thatis,x ∗ is ... solutions of nonlinear singular third -order two-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 323, no. 1, pp. 413–425, 2006. 12 Y. Sun, “Positive solutions of...

Ngày tải lên: 21/06/2014, 05:20

... kind of second- order rational difference equation. With the change of the initial values, we find the successive lengths of positive and negative semicycles for oscillatory solutions of this equation, ... class of second- order nonlinear difference equation Li Dongsheng 1* , Zou Shuliang 1 and Liao Maoxin 2 * Correspondence: lds1010@sina. com 1 School of Economics and Management, University of South China, ... of South China, Hengyang, Hunan 421001, People’s Republic of China Full list of author information is available at the end of the article Abstract In this paper, we consider the rule of trajectory...

Ngày tải lên: 20/06/2014, 22:20

... 1. Hence, beginning with some k ,Equation 2.6 has exactly one positive root corresponding to the imaginary root of Equation 2.5. Now, find the asymptotic of the imaginary roots of Equation 2.5. ... numerator in the vicinity of zero is O(z ν+1 ), and the order of its denominator is O(z ν ), the integral along the left part of contour vanishes. Now, consider the integrals along the remaining three ... real roots. Proof. l is real since it is eigenvalue of self-adjoint operator associated with problem (2.1), (2.2). g k is real by our assumption (A*=A). Hence, the roots of (2.5) are square roots of real...

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... data MIN_VAL: Min value of data TFmax: Max of transformation function TFmin: Min of transformation function OV: Original Value Application Application Training Training Training tunes a neural ... training, and testing. CONTENT CONTENT Introduction Introduction Steps in data forecasting modeling Steps in data forecasting modeling using neural network using neural network Determine ... employed in training the network. The test set, often includes 10% to 30% of training set, is used in testing the generalization. And the verification set is set balance between the needs of enough...

Ngày tải lên: 28/04/2014, 10:18

... contains, in particular, the equation with principal part which coincides with the principal part of the equation of minimal surfaces (1.7.13). The latter is also contained in the third class of equations ... 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...

Ngày tải lên: 31/05/2014, 01:37

... 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 ... 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,...

Ngày tải lên: 20/06/2014, 21:20

... equations in ℝ N . Nonlinear Anal. 59, 173–188 (2004) 19. Rabinowitz, PH: Minimax methods in critical point theory with applications to differential equations. In CBMS Reg Conf Ser in Math, vol. 65,American ... 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 ... . 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 || ∞ ® +∞,ask ® ∞.TheproofofTheorem3.2is complete. Proof of Theorem...

Ngày tải lên: 20/06/2014, 22:20

... type equations. J Differ Eqn. 184(1), 78–96 (2002). doi:10.1006/jdeq.2001.4135 12. Li, CY: Homoclinic orbits of two classes of fourth order semilinear differential equations with periodic nonlinearity. ... existence of global attractor for a class of infinite dimensional nonlinear dissipative dynamical systems. Chin Ann Math B. 26(3), 1–8 (2005) 17. Temam, R: Infinite-Dimensional Dynamical Systems in ... PR China 2 College of Mathematics and Software Science, Sichuan Normal University, Chengdu, Sichuan 610066, PR China Competing interests The author declares that they have no competing interests. Received:...

Ngày tải lên: 20/06/2014, 22:20

... Journal of Inequalities and Applications 2011, 2011:34 http://www.journalofinequalitiesandapplications.com/content/2011/1/34 Page 8 of 12 4. Gajda, Z: On stability of additive mappings. Int J Math ... stability of the Euler-Lagrange functional equation. Chin J Math. 20, 185–190 (1992) 16. Rassias, JM: On the stability of the non-linear Euler-Lagrange functional equation in real normed linear spaces. ... normed spaces. Journal of Inequalities and Applications 2011 2011:34. Park et al. Journal of Inequalities and Applications 2011, 2011:34 http://www.journalofinequalitiesandapplications.com/content/2011/1/34 Page...

Ngày tải lên: 21/06/2014, 01:20

... 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 and Main Result In ... part of cylinder C  S 1 ×R,whereS 1  R/2πZ,wedenote by Γ the class of Jordan curves in C that are homotopic to the circle r  constant. The subclass of Γ composed of those curves lying in A ... systems 1.9 to a form of small perturbation of integrable reversible system. Then a KAM Theorem f or reversible mapping can be applied to the Poincar ´ e mapping of this nearly integrable reversible...

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 ... 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 ... 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 error...

Ngày tải lên: 21/06/2014, 11:20

... 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. ... 2 1 ψ j   1 h k ∞  jk h j  Gw  j − 1 h k ∞  jk Δh j Δw j . 3.16 Solvability of this equation will be examined by means of the contraction mapping theorem in the Banach space of sequences converging towards zero. The following properties of h will play ... 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...

Ngày tải lên: 21/06/2014, 11:20

... Differential Equations, vol. 23, pp. 979–987, 1987. 4 C. P. Gupta, “Solvability of a three-point nonlinear boundary value problem for a second order ordinary differential equation, ” Journal of Mathematical ... nonlinear second- order three-point boundary value problem,” Journal of Mathematical Analysis and Applications, vol. 296, no. 1, pp. 265–275, 2004. 7 Y. Sun, “Positive solutions of nonlinear second- order ... results of 16, 17 to some degree. The main tools used in this paper are Leray-Schauder nonlinear alternative and the fixed point index theory. The rest of the paper is organized as follows. In Section...

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