fourier series transforms and boundary value problems pdf

... Science and Engineering, vol 61-I, Academic Press, New York, 1970 [2] R E Bellman and R E Kalaba, Quasilinearization and Nonlinear Boundary- Value Problems, Modern Analytic and Computional ... convergence for first order initial value problems when the forcing function is the sum of hyperconvex and hyperconcave functions with natural and coupled lower and upper solutions. In this paper ... α n+1 ≤ β n+1 ≤ β n on J,whereα n+1 and β n+1 are solutions of BVPs (3.6)and(3.7), respectively, with α = α n and β = β n . The inequalities (3.2)and(3.4), and (3.15)imply −α  n ≤ f  t,α n

Ngày tải lên: 22/06/2014, 22:20

... Principles and Boundary Value Problems for First-Order Neutral Functional Differential Equations Alexander Domoshnitsky, Abraham Maghakyan, and Roman Shklyar Department of Mathematics and Computer ... in contrast with the cases of ordinary and evenpartial differential equations, do not add so much in problems of existence and uniqueness forboundary value problems with delay differential equations ... neutral functional differential equation 1.1 and on this basis we obtain results on existence and uniqueness of solutions of variousboundary value problems Although several assertions were presented

Ngày tải lên: 22/06/2014, 03:20

... nonlinear boundary value problems for the one- dimensional p-Laplacian,Appl.Math.Lett.14 (2001), no. 2, 189–194. 214 Discrete initial and boundary value problems [10] R. Man ´ asevich and F. Zanolin, ... initial and boundary value problems Example 2.2. Consider the boundary value problem ∆ 2 u(k − 1) = k  u(k)  α +  u(k)  β − A, k ∈ N, u(0) = u(T +1)= 0 (2.23) with p = 2, α>0, 0 ≤ β<1, and ... initial and boundary value problems the literature (see [2, 4, 5, 6, 7, 9, 10, 11] and the references therein). However, only a few papers have discussed the discrete singular case (see [1, 3, 8] and

Ngày tải lên: 23/06/2014, 00:20

... initial value problems (IVPs) and periodic boundary-value problems (BVPs) for this special class of SDEs The index notion for linear SDEs with time-varying coefficients was introduced in [8,16] and ... theory and practice The general form of DAEs is f t, x(t ), x(t ) and its linearization has the form where A . and B .are given matrix functions Equations (1) and (2) can be seen in many real problems, ... an ordinary differential equation and algebraic relations Results on the solvability of the Cauchy problem for (2) can be found in [10]; for the boundary value problems, we can refer to [17] Together

Ngày tải lên: 16/12/2017, 10:52

... AS GENERAL AND PARTICULAR SOLUTIONS 33 If v0  and 0 y0 20, then v  and at 1 2 34 On Earth: v 32t , so v0 tv0 32 at maximum height (when v ) Substituting 0 this value of t and y144 in ... simultaneously the equations x t 45 and x t  we find that 0 1210 2 14.94 ft/s Trang 1616 INTEGRALS AS GENERAL AND PARTICULAR SOLUTIONS With this value of the deceleration and the (as yet) unknown velocity ... answer, and then include without further com-ment the similarly constructed figures for Problems 2 through 9 1 The following sequence of Mathematica 7 commands generates the slope field and the

Ngày tải lên: 20/08/2020, 13:33

... of Solving Boundary Value Problems Chapter FOURIER SERIES AND APPLICATIONS The Need for Fourier Series Periodic Functions Piecewise Continuous Fune- tions Definition of Fourier Series Dirichlet ... Series or Expansions 67 Chapter FOURIER INTEGRALS AND APPLICATIONS The Need for Fourier Integrals The Fourier Integral Equivalent Forms of Fourier’s Integral Theorem Fourier Transforms Fourier ... by Fig 1-4 Fig 1-5 Trang 11CHAP 1] BOUNDARY VALUE PROBLEMS 5 METHODS OF SOLVING BOUNDARY VALUE PROBLEMS There are many methods by which boundary value problems involving linear partial differential

Ngày tải lên: 31/03/2014, 15:23

... developed for handling more general types of nonlinear boundary value problems for ordinaryand functional-differential equations We refer, e.g., to the books [3–5], the articles [6–12], and the series ... solution of the boundary value problem (6) if and only if the value of the vector parameters z ∈ D γ and λ ∈ Λ are such that ∆(z, λ) = 0. Proof It is sufficient to apply Theorem 2 and notice that ... general nonlinearboundary value problems studied in [14] Trang 42 Problem setting and preliminariesWe consider the following system of two nonlinear differential equations with Dirichlet boundary conditions

Ngày tải lên: 20/06/2014, 21:20

... Existence of Positive, Negative, and Sign-Changing Solutions to Discrete Boundary Value Problems Bo Zheng,1 Huafeng Xiao,1 and Haiping Shi2 1 School of Mathematics and Information Sciences, Guangzhou ... two-point boundary value problem are obtained An example is also given to demonstrate our main result 1 Introduction Let , , and  denote the sets of all natural numbers, integers, and real numbers, ... positive and write u > 0 if for all n ∈ 1, T, un ≥ 0, and {n ∈ 1, T: un > 0} / ∅, and similarly, Trang 2u is negative u < 0 if for all n ∈ 1, T, un ≤ 0, and {n ∈ 1,

Ngày tải lên: 21/06/2014, 05:20

... the norm x  max t∈0,T |xt| and P  {x ∈ E : x is concave and nonnegative valued on0, T, and xΔ0  0} Clearly, E is a Banach space with the norm x and P is a cone in E For each x ∈ ... p-Laplacian,” Journal of Mathematical Analysis and Applications, vol 277, no 2, pp 395–404, 2003 2 Y Liu and W Ge, “Twin positive solutions of boundary value problems for finite difference equations ... solutions for m-Laplacian boundary value problems,” Applied Mathematics Letters, vol 12, no 3, pp 11–17, 1999. 5 E R Kaufmann, “Positive solutions of a three-point boundary-value problem on a time

Ngày tải lên: 21/06/2014, 06:20

... differential equation Neumann boundary value problems. 2 Boundary Value Problems Recently, the authors 4 discussed second-order superlinear repulsive singular Neumann boundary value problems by using a ... existence and uniqueness of positive solutions for two classes of nonlinear perturbed Neumann boundary value problems for second-order differential equations. The theorems for Neumann boundary value problems ... Corporation Boundary Value Problems Volume 2010, Article ID 494210, 10 pages doi:10.1155/2010/494210 Research Article Existence and Uniqueness Results for Perturbed Neumann Boundary Value Problems

Ngày tải lên: 21/06/2014, 11:20

... theory,Deng and Shi5 studied the existence and multiplicity of the boundary value problems to aclass of second-order functional difference equations Lu n  fn, u n1, u n , u n−1 1.1with boundary value ... equation boundary value problems with sign changing nonlinearities,” Journal of Computational and Applied Mathematics, vol 169, no 2, pp 345–357, 2004. 3 J Henderson and A Peterson, “Boundary value ... J Yang, B Shi, and D C Zhang, “Existence of positive solutions for boundary value problems of nonlinear functional difference equation with p-Laplacian operator,” Boundary Value Problems, vol 2007,

Ngày tải lên: 21/06/2014, 11:20

... distribution, and reproduction in any medium, provided the original work is properly cited We discuss the existence and uniqueness of the solutions of a second-order m-point nonlocal boundary value problem ... by Bicadze and Samarski˘ı 21, has been addressed by many authors, for instance, 22–32 The multipoint boundary conditions appear in certain problems of thermodynamics, elasticity and wave propagation, ... solution of the boundary value problem 1.1 and 1.2 if −αt ≤ ft, α t, αt, t ∈ 0, 1, pα 0 − qα0 ≤m−2 i1 τiα ηi , pα 1  qα1 ≤m−2 i1 σiα ηi , 2.3 and β ∈ C20,

Ngày tải lên: 21/06/2014, 11:20

... Approximation of Solution of Some m-Point Boundary Value Problems on Time Scales 1 Centre for Advanced Mathematics and Physics, National University of Sciences and Technology (NUST), H-12, Islamabad ... of boundary value problemsBVPson time scales has attracted the attention of many authors; see, for example,5 12 and the references therein for the existence theory of some two-point BVPs, and13–16 ... existence results via upper and lower solutions method and approximation of solutions via generalized quasilinearization method for some three-point boundary value problems on time scales have

Ngày tải lên: 21/06/2014, 16:20

... Provisional PDF corresponds to the article as it appeared upon acceptance Fully formattedPDF and full text (HTML) versions will be made available soon. Multi-point boundary value problems for ... Equations © 2012 Yang and Zhang ; licensee Springer. Trang 2Multi-point boundary value problems for anincreasing homeomorphism and positive homomorphism on time scales Liu Yang∗1,2 and Weiguo Zhang1 ... homeo-morphism and positive homohomeo-morphism. Trang 31 IntroductionWith the development of boundary value problems for differential equations [1–5], dif-ference equations [6, 7], and the theory

Ngày tải lên: 21/06/2014, 17:20

... of positive and dead core solutions of singular second-order differential equations with a parameter was discussed for Dirichlet boundary conditions in1,2 and for mixed and Robin boundary conditions ... 262854, 17 pagesdoi:10.1155/2010/262854 Research Article Positive and Dead-Core Solutions of Two-Point Singular Boundary Value Problems with φ-Laplacian Svatoslav Stan ˇek Department of Mathematical ... the existence and multiplicity of positive and dead core solutions of the singular differential equation u λgu satisfying the boundary conditions u0  0, βu1  αu1  A and u0  1,

Ngày tải lên: 21/06/2014, 18:20

... Article Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales Meiqiang Feng,1 Xuemei Zhang,2, 3 Xianggui Li,1 and Weigao Ge3 ... solutions for a class of singular boundary value problems on time scales The results significantly extend and improve many known results for both the continuous case and more general time scales We ... sufficient and necessary conditions to guarantee the existence of positive solutions for singular boundary value problem on time scales So it is interesting and important to discuss these problems

Ngày tải lên: 21/06/2014, 20:20

... Approximation Approach to Eigenvalue Intervals for Singular Boundary Value Problems with Sign Changing and Superlinear Nonlinearities Haishen L ¨u,1 Ravi P Agarwal,2, 3 and Donal O’Regan4 1 Department ... Mathematical Analysis and Applications, vol 181, no 3, pp 684–700, 1994. 5 H L ¨u, D O’Regan, and R P Agarwal, “An approximation approach to eigenvalue intervals for singular boundary value problems with ... other hand, a1 1  1 01/√s ds  3 and let R j  x 2j − 3, so we have Trang 33Example 3.2 Consider the boundary value problemTo see this, let β  min{1/2, α/2}, g1t, r  1/r β  π α , and g2t,

Ngày tải lên: 21/06/2014, 20:20

... pagesdoi:10.1155/2009/191627 Research Article Existence and Uniqueness of Smooth Positive Solutions to a Class of Singular m-Point Boundary Value Problems Xinsheng Du and Zengqin Zhao School of Mathematics Sciences, ... investigates the existence and uniqueness of smooth positive solutions to a class of singular m-point boundary value problems of second-order ordinary differential equations A necessary and sufficient condition ... 1 Introduction and the Main Results In this paper, we will consider the existence and uniqueness of positive solutions to a class of second-order singular m-point boundary value problems of the

Ngày tải lên: 21/06/2014, 20:20