研究了带有界面条件的弱非线性边值问题,借助Schauder不动点定理建立带有界面条件的弱非线性边值问题的上下解理论,通过边界层函数法构造形式渐近解, 证明解的存在性.
吴成龙
. 一类带有界面条件的奇异摄动弱非线性边值问题[J]. 华东师范大学学报（自然科学版）, 2016
, 2016(3)
: 27
-38
.
DOI: 2016.03.004
In this paper we study a class of weakly nonlinear boundary value problems with interface conditions. By means of the Schauder fixed point theorem we establish the theorem about a weakly nonlinear boundary value problem with interface conditions. By the method of boundary layer function, the formal asymptotic solution is constructed, which is used to prove the existence of the solution
[1]莫嘉琪. 关于非线性方程$\varepsilony''=f(x,y,y',\varepsilon)$奇异摄动边值问题解的估计~[J]. 数学年刊,1984, 5A (1): 73-77.
[2] MO J Q. Generalized solution of singularly perturbed problems for nonlinear reaction diffusion equation [J]. Journal of Anhui Normal University(Natural Science), 2014, 2: 103-107.
[3] 杜增吉, 莫嘉琪: 一类扰动发展方程近似解~[J]. 物理学报, 2012, 61(15):155202.
[4] 周明儒, 杜增吉, 王广瓦. 奇异摄动中的微分不等式理论~[M]. 北京:科学出版社, 2012.
[5] 倪明康, 林武忠. 奇异摄动问题中的渐近理论~[M]. 北京: 高等教育出版社,2009.
[6] MIKHAILOV M, \"{OZISIK M. Unified Analysis and Solution of Heat and Mass Diffusion[M]. New York: Dover, 1994.
[7] DE FALCO C, O'RIORDAN E. Interior layers in a reaction-diffusion equation with a discontinuous diffusion coefficient [J]. Int J Numer Anal Model, 2010, 7: 444-461.
[8] XIE F. An interface problem with singular perturbation on a subinterval [J]. Boundary Value Problems, 2014, 2014: 201.
[9] 丁云海, 倪明康. 具有不连续源的弱非线性奇异摄动边值问题~[J].山东大学学报, 2012, 47(2): 8-13.
[10] LIN H X, XIE F. Singularly perturbed second order semilinear boundary value problems with interface conditions [J]. Boundary Value Problems, 2015, 2015: 47.
[11] KELLY W G, PETERSON A C. The Theory of Differential Equations [M].New York: Springer-Verlag, 2010.
中国综合性科技类核心期刊(北大核心)