Giải pháp Dương của Phương trình Vi phân Phi tuyến Bậc th với Điều kiện Biên Không Địa phương và Ảnh hưởng Bất ngờ

Lakshmikantham V, Baĭnov DD, Simeonov PS: Theory of Impulsive Differential Equations, Series in Modern Applied Mathematics. World Scientific, Teaneck, NJ, USA; 1989:xii+273. Benchohra M, Henderson J, Ntouyas S: Impulsive Differential Equations and Inclusions, Contemporary Mathematics and Its Applications. Volume 2. Hindawi, New York, NY, USA; 2006:xiv+366. Baĭnov DD, Simeonov PS: Systems with Impulse Effect, Ellis Horwood Series: Mathematics and Its Applications. Ellis Horwood, Chichester, UK; 1989:255. Samoĭlenko AM, Perestyuk NA: Impulsive Differential Equations, World Scientific Series on Nonlinear Science. Series A: Monographs and Treatises. Volume 14. World Scientific, River Edge, NJ, USA; 1995:x+462. Lin X, Jiang D: Multiple positive solutions of Dirichlet boundary value problems for second order impulsive differential equations. Journal of Mathematical Analysis and Applications 2006, 321(2):501-514. 10.1016/j.jmaa.2005.07.076 Zhang X, Feng M, Ge W: Existence of solutions of boundary value problems with integral boundary conditions for second-order impulsive integro-differential equations in Banach spaces. Journal of Computational and Applied Mathematics 2010, 233(8):1915-1926. 10.1016/j.cam.2009.07.060 Zhang X, Yang X, Ge W: Positive solutions of n th-order impulsive boundary value problems with integral boundary conditions in Banach spaces. Nonlinear Analysis. Theory, Methods & Applications 2009, 71(12):5930-5945. 10.1016/j.na.2009.05.016 Agarwal RP, O'Regan D: Multiple nonnegative solutions for second order impulsive differential equations. Applied Mathematics and Computation 2000, 114(1):51-59. 10.1016/S0096-3003(99)00074-0 Liu B, Yu J: Existence of solution of m -point boundary value problems of second-order differential systems with impulses. Applied Mathematics and Computation 2002, 125(2-3):155-175. 10.1016/S0096-3003(00)00110-7 Feng M, Du Bo, Ge W: Impulsive boundary value problems with integral boundary conditions and one-dimensional p -Laplacian. Nonlinear Analysis. Theory, Methods & Applications 2009, 70(9):3119-3126. 10.1016/j.na.2008.04.015 Lee E, Lee Y: Multiple positive solutions of singular two point boundary value problems for second order impulsive differential equations. Applied Mathematics and Computation 2004, 158(3):745-759. 10.1016/j.amc.2003.10.013 Zhang X, Ge W: Impulsive boundary value problems involving the one-dimensional p -Laplacian. Nonlinear Analysis. Theory, Methods & Applications 2009, 70(4):1692-1701. 10.1016/j.na.2008.02.052 Feng M, Pang H: A class of three-point boundary-value problems for second-order impulsive integro-differential equations in Banach spaces. Nonlinear Analysis. Theory, Methods & Applications 2009, 70(1):64-82. 10.1016/j.na.2007.11.033 Feng M, Xie D: Multiple positive solutions of multi-point boundary value problem for second-order impulsive differential equations. Journal of Computational and Applied Mathematics 2009, 223(1):438-448. 10.1016/j.cam.2008.01.024 Cannon JR: The solution of the heat equation subject to the specification of energy. Quarterly of Applied Mathematics 1963, 21: 155-160. Ionkin NI: The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition. Differential Equations 1977, 13(2):294-304. Chegis RYu: Numerical solution of a heat conduction problem with an integral condition. Lietuvos Matematikos Rinkinys 1984, 24(4):209-215. Il'in V, Moiseev E: Nonlocal boundary value problem of the second kind for a Sturm-Liouville operator. Differential Equations 1987, 23: 979-987. Eloe PW, Ahmad B:Positive solutions of a nonlinear order boundary value problem with nonlocal conditions. Applied Mathematics Letters 2005, 18(5):521-527. 10.1016/j.aml.2004.05.009 Ma R, Wang H: Positive solutions of nonlinear three-point boundary-value problems. Journal of Mathematical Analysis and Applications 2003, 279(1):216-227. 10.1016/S0022-247X(02)00661-3 Ma R, Thompson B: Positive solutions for nonlinear m -point eigenvalue problems. Journal of Mathematical Analysis and Applications 2004, 297(1):24-37. 10.1016/j.jmaa.2003.12.046 Pang C, Dong W, W Z: Green's function and positive solutions of n th order m -point boundary value problem. Applied Mathematics and Computation 2006, 182(2):1231-1239. 10.1016/j.amc.2006.05.010 Yang J, Wei Z: Positive solutions of n th order m -point boundary value problem. Applied Mathematics and Computation 2008, 202(2):715-720. 10.1016/j.amc.2008.03.009 Feng M, Ge W: Existence results for a class of n th order m -point boundary value problems in Banach spaces. Applied Mathematics Letters 2009, 22(8):1303-1308. 10.1016/j.aml.2009.01.047 He X, Ge W: Triple solutions for second-order three-point boundary value problems. Journal of Mathematical Analysis and Applications 2002, 268(1):256-265. 10.1006/jmaa.2001.7824 Guo Y, Ge W: Positive solutions for three-point boundary value problems with dependence on the first order derivative. Journal of Mathematical Analysis and Applications 2004, 290(1):291-301. 10.1016/j.jmaa.2003.09.061 Cheung W, Ren J: Positive solution for m -point boundary value problems. Journal of Mathematical Analysis and Applications 2005, 303(2):565-575. 10.1016/j.jmaa.2004.08.056 Gupta C: A generalized multi-point boundary value problem for second order ordinary differential equations. Applied Mathematics and Computation 1998, 89(1–3):133-146. Feng W: On an m -point boundary value problem. Nonlinear Analysis. Theory, Methods & Applications 1997, 30(8):5369-5374. 10.1016/S0362-546X(97)00360-X Feng W, Webb JRL: Solvability of m -point boundary value problems with nonlinear growth. Journal of Mathematical Analysis and Applications 1997, 212(2):467-480. 10.1006/jmaa.1997.5520 Feng W, Webb JRL: Solvability of three point boundary value problems at resonance. Nonlinear Analysis. Theory, Methods & Applications 1997, 30(6):3227-3238. 10.1016/S0362-546X(96)00118-6 Feng M, Ji D, Ge W: Positive solutions for a class of boundary-value problem with integral boundary conditions in Banach spaces. Journal of Computational and Applied Mathematics 2008, 222(2):351-363. 10.1016/j.cam.2007.11.003 Zhang G, Sun J: Positive solutions of m -point boundary value problems. Journal of Mathematical Analysis and Applications 2004, 291(2):406-418. 10.1016/j.jmaa.2003.11.034 Feng M, Ge W: Positive solutions for a class of m -point singular boundary value problems. Mathematical and Computer Modelling 2007, 46(3-4):375-383. 10.1016/j.mcm.2006.11.009 Ahmad B, Nieto JJ: Existence results for nonlinear boundary value problems of fractional integrodifferential equations with integral boundary conditions. Boundary Value Problems 2009, 2009: 11. Webb JRL, Infante G, Franco D: Positive solutions of nonlinear fourth-order boundary-value problems with local and non-local boundary conditions. Proceedings of the Royal Society of Edinburgh 2008, 138(2):427-446. Zhang X, Liu L: A necessary and sufficient condition for positive solutions for fourth-order multi-point boundary value problems with p -Laplacian. Nonlinear Analysis. Theory, Methods & Applications 2008, 68(10):3127-3137. 10.1016/j.na.2007.03.006 Bai ZB, Ge W: Existence of positive solutions to fourth order quasilinear boundary value problems. Acta Mathematica Sinica 2006, 22(6):1825-1830. 10.1007/s10114-005-0806-z Bai Z: The upper and lower solution method for some fourth-order boundary value problems. Nonlinear Analysis. Theory, Methods & Applications 2007, 67(6):1704-1709. 10.1016/j.na.2006.08.009 Ma R, Wang H: On the existence of positive solutions of fourth-order ordinary differential equations. Applicable Analysis 1995, 59(1–4):225-231. Bai Z: Iterative solutions for some fourth-order periodic boundary value problems. Taiwanese Journal of Mathematics 2008, 12(7):1681-1690. Bai Z: Positive solutions of some nonlocal fourth-order boundary value problem. Applied Mathematics and Computation 2010, 215(12):4191-4197. 10.1016/j.amc.2009.12.040 Liu L, Zhang X, Wu Y: Positive solutions of fourth-order nonlinear singular Sturm-Liouville eigenvalue problems. Journal of Mathematical Analysis and Applications 2007, 326(2):1212-1224. 10.1016/j.jmaa.2006.03.029 Zhang X, Ge W: Positive solutions for a class of boundary-value problems with integral boundary conditions. Computers & Mathematics with Applications 2009, 58(2):203-215. 10.1016/j.camwa.2009.04.002 Guo D, Lakshmikantham V: Nonlinear Problems in Abstract Cones, Notes and Reports in Mathematics in Science and Engineering. Volume 5. Academic Press, Boston, Mass, USA; 1988:viii+275.