一类非线性三阶奇摄动边值问题解的存在性和渐近估计
Existence and Asymptotic Estimates of Solutions for a Class of Nonlinear Third-Order Singularly Perturbed Boundary Value Problems
DOI: 10.12677/PM.2021.116112, PDF, HTML, 下载: 334  浏览: 471  国家自然科学基金支持
作者: 张瑞燕：西北师范大学数学与统计学院，甘肃 兰州
关键词: 三阶；奇异摄动；存在性；渐近估计；Third-Order； Singularly Perturbed； Existence； Asymptotic Estimates
摘要: 本文研究一类三点边值条件下非线性三阶奇摄动边值问题 解的存在性和渐近估计, 其中0 < η < 1，0 < ξη < 1. 通过构造一个恰当的广义上下解对和运用Nagumo 条件和边界层函数,我们得到上述问题解的存在性,并且给出了解的一致有效渐近估计.
Abstract: This paper is devoted to study the existence and asymptotic estimates of solutions for a class of nonlinear third-order singularly perturbed boundary value problems with three-point boundary value conditions where 0 < η < 1, 0 < ξη < 1. By constructing an appropriate generalized upper- and lower-solution pair and employing the Nagumo conditions and boundary layer functions, we obtain the existence of solutions to the above problem and give uniformly valid asymptotic estimates of the solutions.
文章引用：张瑞燕. 一类非线性三阶奇摄动边值问题解的存在性和渐近估计[J]. 理论数学, 2021, 11(6): 979-989. https://doi.org/10.12677/PM.2021.116112

参考文献

[1] Guo, L.J., Sun, J.P. and Zhao, Y.H. (2008) Existence of Positive Solution for Nonlinear Third- Order Three-Point Boundary Value Problem. Nonlinear Analysis: Theory, Methods and Ap- plications, 68, 3151-3158.
https://doi.org/10.1016/j.na.2007.03.008
[2] Torres, F.J. (2013) Positive Solutions for a Third-Order Three Point Boundary Value Problems. Electronic Journal of Differential Equations, 2013, 1-11.
[3] Sun, Y.P. (2005) Positive Solutions of Singular Third-Order Three-Point Boundary Value Problem. Journal of Mathematical Analysis and Applications, 306, 589-603.
https://doi.org/10.1016/j.jmaa.2004.10.029
[4] Palamides, A.P. and Smyrlis, G. (2008) Positive Solutions to a Singular Third-Order Three- Point Boundary Value Problem with an Indefinitely Signed Green’s Function. Nonlinear Anal- ysis: Theory, Methods and Applications, 68, 2104-2118.
https://doi.org/10.1016/j.na.2007.01.045
[5] Sun, J.P., Ren, Q.Y. and Zhao, Y.H. (2010) The Upper and Lower Solution Method for Non- linear Third-Order Three-Point Boundary Value Problem. Electronic Journal of Qualitative Theory of Differential Equations, 2010, 1-8.
https://doi.org/10.14232/ejqtde.2010.1.26
[6] Henderson, J. and Kosmatov, N. (2014) Three-Point Third-Order Problems with a Sign- Changing Nonlinear Term. Electronic Journal of Differential Equations, 2014, 1-10.
[7] Graef, J.R. and Yang, B. (2005) Multiple Positive Solutions to a Three Point Third Order Boundary Value Problem. Discrete and Continuous Dynamical Systems, 2005, 337-344.
[8] Ma, R.Y. (1999) Positive Solutions of a Nonlinear Three-Point Boundary-Value Problem. Elec- tronic Journal of Differential Equations, 1998, 1-8.
[9] Lin, S.-R. (2011) The Singular Perturbation of Boundary Value Problem for Third-Order Nonlinear Vector Integro-Differential Equation and Its Application. Applied Mathematics and Computation, 218, 1746-1751.
https://doi.org/10.1016/j.amc.2011.06.056

为你推荐