the solution of second order differential equation
Báo cáo hóa học: " Research Article On the Spectrum of Almost Periodic Solution of Second-Order Neutral Delay Differential Equations with Piecewise Constant of Argument" ppt
... expressions of x2n,x2n1,y2n,ωt, and xt are important in the process of studying the spectrum containment of the almost periodic solution of 1.1. Before giving the main theorem, we list the ... B}.We postpone the proof of this theorem to the next section.3. The Proof of Main TheoremTo show the Main Theorem, we need some more lemmas.Lemma 3.1. Let f ∈APR,thenσbfi2n,σbfi2n1,σbh2n,σbh2n1 ... ∈ R, which guarantees the uniqueness of solution of 1.1 and cannot beomitted.To study the spectrum of almost periodic solution of 1.1, we firstly study the solution of 1.1.Letf1nn1nsnfσdσ...
- 14
- 335
- 0
Báo cáo toán học: " Lyapunov-type inequalities for a class of even-order differential equations" doc
... interval symmetrizes about the origin. Then, similar to the proof of (2.9), wecan verify the condition f(α) = f(β), and the other conditions in Lemma 2.2 are satisfiedall the way. Hence, it also ... contributionsQZ 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 similarmethod 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...
- 12
- 402
- 0
Báo cáo hóa học: "Research Article Iterative Solutions of Singular Boundary Value Problems of Third-Order Differential Equation" potx
... and the existence results of nontrivial solutions and positive solutions are given by means of the topological degreetheory. Motivated by the above works, we consider the singular third -order ... “Existence of solutions for a class of third -order nonlinear boundary valueproblems,” 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...
- 10
- 305
- 0
báo cáo hóa học:" Research Article Regularly Varying Solutions of Second-Order Difference Equations with Arbitrary Sign Coefficient" ppt
... multiple of k.On the other hand, in the remaining two cases, the study of the regular variation of the solutions gives the additional information that the positive solutions, even if they are ... MRV2M∞,0. The above theorem shows how the study of the regular variation of the solutionsand the M-classification supplement each other to give an asymptotic description of nonoscillatory solutions. ... general equations. The aim of this section is to analyze the relations between the classification of the eventually positive solutions according to their regularly varyingbehavior, and the M-classification....
- 16
- 309
- 0
báo cáo hóa học:" Research Article Minimal Nonnegative Solution of Nonlinear Impulsive Differential Equations on Infinite Interval" pot
... economics. The theory of impulsive differential equations hasbecome an important area of investigation in the recent years and is much richer than the corresponding theory of differential equations. ... mentioning the worksby Guo 31.In31, Guo investigated the minimal nonnegative solution of the followinginitial value problem for a second order nonlinear impulsive integrodifferential equation of Volterra ... we will use the cone theory andmonotone iterative technique to investigate the existence of minimal nonnegative solution for a class of second- order nonlinear impulsive differential equations on...
- 15
- 372
- 0
báo cáo hóa học: " Study of the asymptotic eigenvalue distribution and trace formula of a second order operatordifferential equation" ppt
... 1+hν2⎤⎥⎦.(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 thisseries is ∞, then ... verified that in the vicinity of zero, the function g(z) is of order O (zν).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...
- 22
- 334
- 0
Báo cáo hóa học: " Positive solutions of the three-point boundary value problem for fractional-order differential equations with an advanced argument" ppt
... fractional -order models have proved to be more accurate than integer- order models, i.e., there are more degrees of freedom in the fractional -order models. Inconsequence, the subject of fractional differential ... 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 ... mentioning that the condit ions of our theorems are easily toverify, so they are applicable to a variety of problems, see Examples 4.1 and 4.2. The proof of our main resul ts is based upon the following...
- 11
- 343
- 0
báo cáo hóa học:" Research Article Biorthogonal Systems Approximating the Solution of the Nonlinear Volterra Integro-Differential Equation" doc
... εk,3.7and therefore,Tzk−1− zk≤ εk3.8as announced. The next result is used in order to establish the fact that the sequence defined inTheorem 3.1 approximates the solution of the nonlinear ... in order to approximate the solution of the nonlinear Volterra integro-differential equation. We define, following a fixed-point approach,a sequence of functions which approximate the solution of ... estimate the rate of convergence of the sequence of projections. For this purpose, consider the dense subset {ti}i≥1 of distinct points in 0, 1 andlet Tnbe the set {t1, ,tn} ordered...
- 9
- 336
- 0
báo cáo hóa học:" Research Article Error Bounds for Asymptotic Solutions of Second-Order Linear Difference Equations II: The First Case" pot
... 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: ... still open. The purpose of this and the next paper Errorbounds for asymptotic solutions of second- order linear difference equations II: the second case is to estimate error bounds for solutions ... 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 to the...
- 19
- 377
- 0
Tìm thêm: hệ việt nam nhật bản và sức hấp dẫn của tiếng nhật tại việt nam xác định các mục tiêu của chương trình xác định các nguyên tắc biên soạn khảo sát chương trình đào tạo của các đơn vị đào tạo tại nhật bản khảo sát chương trình đào tạo gắn với các giáo trình cụ thể xác định thời lượng học về mặt lí thuyết và thực tế tiến hành xây dựng chương trình đào tạo dành cho đối tượng không chuyên ngữ tại việt nam điều tra đối với đối tượng giảng viên và đối tượng quản lí điều tra với đối tượng sinh viên học tiếng nhật không chuyên ngữ1 khảo sát thực tế giảng dạy tiếng nhật không chuyên ngữ tại việt nam xác định mức độ đáp ứng về văn hoá và chuyên môn trong ct mở máy động cơ rôto dây quấn hệ số công suất cosp fi p2 đặc tuyến mômen quay m fi p2 đặc tuyến dòng điện stato i1 fi p2 động cơ điện không đồng bộ một pha sự cần thiết phải đầu tư xây dựng nhà máy thông tin liên lạc và các dịch vụ từ bảng 3 1 ta thấy ngoài hai thành phần chủ yếu và chiếm tỷ lệ cao nhất là tinh bột và cacbonhydrat trong hạt gạo tẻ còn chứa đường cellulose hemicellulose chỉ tiêu chất lượng theo chất lượng phẩm chất sản phẩm khô từ gạo của bộ y tế năm 2008