... Order BoundaryValue Problems This section is devoted to the study of the second order boundaryvalue problem(BVP)Heikkilä BoundaryValueProblems 2011, 2011:24http://www.boundaryvalueproblems.com/content/2011/1/24Page ... =1,2,u1 u2, and v1 v2.Heikkilä BoundaryValueProblems 2011, 2011:24http://www.boundaryvalueproblems.com/content/2011/1/24Page 15 of 19 Example 5.1. Determine the smallest and greatest ... smallest and greatest solutions of the second order initial and boundaryvalue problems, and dependence of these solutions on the data are studiedin Sections 5 and 6. Applications to impulsive problems...
... America).Keller, H.B. 1968,Numerical Methods for Two-Point Boundary- Value Problems (Waltham, MA:Blaisdell). 758Chapter 17. Two Point BoundaryValue Problems Sample page from NUMERICAL RECIPES IN C: ... form of the boundary conditions (17.0.2), can write a function thatgenerates a complete set of N starting values y, satisfying the boundary conditionsat x1, from an arbitrary vector value of ... mismatch, and n2for the partial derivatives. Each new cycle requires a new round of n2+1integrations. This illustrates the enormous extra effort involved in solving two point boundary value problems...
... Equations 140.3 BoundaryValueProblems 260.4 Singular BoundaryValueProblems 380.5 Green’s Functions 43Chapter Review 51Miscellaneous Exercises 51CHAPTER 1 FourierSeriesand Integrals 591.1 ... Functions andFourierSeries 591.2 Arbitrary Period and Half-Range Expansions 641.3 Convergence of FourierSeries 731.4 Uniform Convergence 791.5 Operations on FourierSeries 851.6 Mean Error and ... Equations0.3 BoundaryValue Problems A boundaryvalue problem in one dimension is an ordinary differential equa-tion together with conditions involving values of the solution and/ or its deriv-atives...
... Luong and Loi: Initial boundaryvalueproblems for second order parabolic systems incylinders with polyhedral base. BoundaryValueProblems 2011 2011:56.Luong and Loi BoundaryValueProblems ... of vector-valued func-tions u defined in QTwith the normLuong and Loi BoundaryValueProblems 2011, 2011:56http://www.boundaryvalueproblems.com/content/2011/1/56â 2011 Luong and Loi; licensee ... s and a.e. (x, t) ẻ QT.In this article, we study the following problem:ut+ L(x, t; D)u = f in QT,(2)Luong and Loi BoundaryValueProblems 2011, 2011:56http://www.boundaryvalueproblems.com/content/2011/1/56Page...
... for handling more general types of nonlinear boundaryvalueproblems for ordinary and functional-differential equations. We refer, e.g., to the books [3–5], the articles [6–12], and the series ... theory of boundary- value problems. River Edge, NJ: World Scientific Publishing Co. Inc. 2000.6. Augustynowicz, A, Kwapisz, M: On a numerical-analytic method of solving of boundaryvalue problemfor ... of three-point nonlinear boundary value problems. Nel¯ın¯ı˘ın¯ı Koliv. 7(3):395–413 (2004)12. Ront´o, A, Ront´o, M: On a Cauchy-Nicoletti type three-point boundaryvalue problem for linear differ-ential...
... to that of Lemma 2.2 and will omit it here.Li and Dong BoundaryValueProblems 2011, 2011:59http://www.boundaryvalueproblems.com/content/2011/1/59Page 7 of 18 By (2.12) and (2.13), we getσ ... ||u||, u ẻ P 1 and ||Tu|| ||u||, u ẻ P 2,or(ii)||Tu|| ||u||, u ẻ P 1 and ||Tu|| ||u||, u ẻ P 2Li and Dong BoundaryValueProblems 2011, 2011:59http://www.boundaryvalueproblems.com/content/2011/1/59Page ... {g0,g∞},Li and Dong BoundaryValueProblems 2011, 2011:59http://www.boundaryvalueproblems.com/content/2011/1/59Page 11 of 18 Lemma 2.4. Suppose that (H1) is satisfied, for all t, s ẻ I and i...
... to a class of fractional boundary value problems. BoundaryValueProblems 2011 2011:25.Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page ... obvious.Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page 6 of 9 In this case, the boundaryvalue problem is nonautonomous, and thus, this ... continuous and nondecreasing and satisfies ψ(u)>0foru > 0 and ψ(0) = 0. Con-sequently,φ∈J.Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page...
... to a class of fractional boundary value problems. BoundaryValueProblems 2011 2011:25.Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page ... continuous and nondecreasing and satisfies ψ(u)>0foru > 0 and ψ(0) = 0. Con-sequently,φ∈J.Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page ... u(1)= u(0)=0,(10)Caballero et al. BoundaryValueProblems 2011, 2011:25http://www.boundaryvalueproblems.com/content/2011/1/25Page 8 of 9 andtheyprovedtheexistenceofpositivesolutionsbymeansoftheKrasnosel’skiifixed-point...
... Corporation Boundary Value Problems Volume 2010, Article ID 521070, 2 pagesdoi:10.1155/2010/521070EditorialDegenerate and Singular Differential Operatorswith Applications to BoundaryValue Problems Claudianor ... Problems Claudianor Oliveira Alves1 and Vicentáiu Radulescu2, 31Unidade AcademicadeMatematica e Estatstica, Universidade Federal de Campina Grande,58109-970 Campina Grande, PB, Brazil2Institute ... singularities in nonlinear PDEs, and Lane-Emden-Fowler-type equationswith convection and singular potential. We would like to thank the authors for their excellentcontributions and patience in assisting...
... positive and write u>0 if for all n ∈1,T,un ≥ 0, and {n ∈ 1,T: un > 0}/ ∅, and similarly, 2 BoundaryValue Problems u is negative u<0 if for all n ∈1,T,un ≤ 0, and {n ... Zheng and Q. Zhang, “Existence and multiplicity of solutions of second-order difference boundary value problems, ” Acta Applicandae Mathematicae, vol. 110, no. 1, pp. 131–152, 2010.6 X. Cai and ... point boundary value problems, ” Applied Mathematics and Computation, vol. 180, no. 1, pp. 318–329, 2006.8 H. Liang and P. Weng, “Existence and multiple solutions for a second-order difference boundary value...
... 3.3.2 4 BoundaryValue Problems iii xt ≥ T − t/Tx, t ∈ 0,T.iv xt is decreasing on 0,T.The proof is similar to the proofs of Lemma 2.3 and Theorem 3.1 in 7, and is omitted.Fix ... 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 boundaryvalueproblems for finite difference equationswith ... solutions for m-Laplacian boundaryvalue problems, ” AppliedMathematics Letters, vol. 12, no. 3, pp. 11–17, 1999.5 E. R. Kaufmann, “Positive solutions of a three-point boundary- value problem on a...
... 1T4.1 BoundaryValueProblems 1710 R. P. Agarwal, M. Bohner, and W T. Li, Nonoscillation and Oscillation: Theory for Functional DifferentialEquations, vol. 267 of Monographs and Textbooks ... Textbooks in Pure and Applied Mathematics, Marcel Dekker, NewYork, NY, USA, 2004.11 H R. Sun, L T. Tang, and Y H. Wang, “Eigenvalue problem for p-Laplacian three-point boundary valueproblems on ... Journal of Mathematical Analysis and Applications, vol. 331, no. 1, pp.248–262, 2007.12 L. Jiang and Z. Zhou, “Existence of weak solutions of two-point boundaryvalueproblems for second-order...