the application of second order differential equation

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 21/06/2014, 20:20

... interval symmetrizes about the origin. Then, similar to the proof of (2.9), we can verify the condition f  (α) = f  (β), and the other conditions in Lemma 2.2 are satisfied all the way. Hence, it also ... contributions QZ carried out the theoretical proof and drafted the manuscript. XH participated in the design and coordination. Both of the two authors read and approved the final manuscript. References [1] ... [α, β], too. Then, by a similar method to the proof of (2.3) together with Lemma 2.2, we can obtain (2.4) immediately. For the other ordinary cases, i.e., a = 0, we only need to move the interval...

Ngày tải lên: 20/06/2014, 21:20

... and the 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 ... “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 ... 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 Analysis and Applications,...

Ngày tải lên: 21/06/2014, 05:20

... while all the regularly varying solutions of index 1 are asymptotic to a positive multiple of k. On the other hand, in the remaining two cases, the study of the regular variation of the solutions ... examined by means of the contraction mapping theorem in the Banach space of sequences converging towards zero. The following properties of h will play a crucial role in the proof. The first two are ... 1 α  α−1  . 5.2 Proof. The main idea of the proof is the analogous of the linear case, apart from some additional technical problems. We omit all the details, pointing out only the main differences. Necessity Set...

Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 21/06/2014, 20:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 22/06/2014, 22:20

Ngày tải lên: 13/08/2014, 16:20

Ngày tải lên: 21/06/2014, 20:20

... 1+hν 2 ⎤ ⎥ ⎦ . (2:7) Further , let N be the 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 ... verified that in the vicinity of zero, the function g(z) is of order O (z ν ). By virtue of this asymptotic and because g(z) is an odd function, the integral along the left-hand side of the contour ... δ >0. Then, we can state the following theorem. Theorem 3.2. Let the conditions of Theorem 2.1, (3.6) and (3.7) hold. If the operator- value function q(t) has properties 1-3, then the following...

Ngày tải lên: 21/06/2014, 02:20

... 11 as an important area of investigation. For the general theory and applications of integer order differential equations wit h deviat ed arguments, we refer the reader to the refer- ences [39-45]. As ... fractional -order models. In consequence, the subject of fractional differential equations is gaining much impor- tance and attention. For details, see [18-36] and the references therein. Differential equations ... equations.Toidentifyafew,wereferthereaderto [2-13] and the references therein. Fractional differential equations arise in many engineering and scientific disciplines as the mathematical modeling of systems and processes in the fields of ph...

Ngày tải lên: 21/06/2014, 03:20

... 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: ... Asymptotic 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 ... solutions to 1.2 is still open. The purpose of this and the next paper Error bounds for asymptotic solutions of second- order linear difference equations II: the second case is to estimate error...

Ngày tải lên: 21/06/2014, 11:20

Ngày tải lên: 22/06/2014, 02:20

... Michael J. Wallace.) The second instruments are the two set of speaking tests. The first one is the final tests of the three previous semesters (pre-tests) and the other is the final semester ... V. The design of the study: The study is divided into three parts, which are presented as follows. Part A is the introduction, which states the background to the study, the statement of the ... foremost objective of the study is for the sake of the students. Besides, the study is expected to serve as a source of reference for teachers of English on the teaching of speaking skills,...

Ngày tải lên: 29/01/2014, 10:58

Ngày tải lên: 14/03/2014, 13:20

... since the presence of the weak degeneracy poses an obstacle to the improvement of the differential properties of the functions forming the equation. This monograph is not a survey of the theory of ... degenerate equations. We then establish 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 ... depend on the behavior of the right side of the equation. It is shown in [163] that these conditions are inherent in the nature of the problem. §5. Estimates of IV ul on the boundary by means of local...

Ngày tải lên: 31/05/2014, 01:37

... statistical analysis of the capacity of N∗Nakagami-m channels. Specifically, we have studied the influence of the severity of fading and the number of hops on the PDF, CDF, LCR, and ADF of the channel capacity. ... Ψ (1) (·) is the first derivative of the Digamma function Ψ(·) [33, Equation (8.360)]. In order to derive the PDF of the capacity of N∗Nakagami-m channels, we need to find the PDF p Ξ 2 ∞ (z) of the squared ... levels r. Furthermore, the variance of the channel capacity decreases by increasing the number of hops, while increase in the severity of fading has an opposite influence on the variance of the channel...

Ngày tải lên: 20/06/2014, 20:20