一类二阶拟线性边值问题的可解性

姚庆六

doi:10.3879/j.issn.1000-0887.2009.08.012

一类二阶拟线性边值问题的可解性

doi: 10.3879/j.issn.1000-0887.2009.08.012

姚庆六

南京财经大学应用数学系,南京 210003

详细信息

作者简介:
姚庆六(1946- ),男,上海人,教授(E-mail:yaoqingliu2002@hotmail.com).

中图分类号: O175.8
计量
- 文章访问数: 1541
- HTML全文浏览量: 125
- PDF下载量: 769
- 被引次数: 0
出版历程
- 收稿日期: 2008-10-11
- 修回日期: 2009-06-14
- 刊出日期: 2009-08-15

Solvability of a Class of Second-Order Quasilinear Boundary Value Problems

YAO Qing-liu

Department of Applied Mathematics, Nanjing University of Finance and Economics, Nanjing 210003, P. R. China

摘要

摘要: 当非线性项奇异和无穷远处的极限增长函数存在时，考察了一类二阶拟线性边值问题．通过引入非线性项在有界集合上的高度函数，并且考察高度函数的积分,证明了一个解的存在定理．该定理表明当极限增长函数的积分具有适当值时此问题有一个解．
- 拟线性常微分方程 /
- 两点边值问题 /
- 可解性 /
- Lebesgue控制收敛定理
Abstract: A class of second-order quasilinear boundary value problems was considered when the non-linear term is singular and the limit growth function at infinite exists. By introducing the height function of nonlinear term on bounded set and considering integration of the height function, an existence theorem of solution was proved. The existence theorem shows that the problem has a solution if the integration of the limit growth function has appropriate value.
- quasilinear ordinary differential equation /
- two-point boundary value problem /
- solvability /
- Lebesgue dominated convergence theorem

HTML全文

参考文献(16)

[1]	Gelfand I N.Some problems in the theory of quasilinear equations[J].Trans Amer Math Soc,1963,29(2):295-381.
[2]	Bobernes J,Eberly D.Mathematical Problems From Combustion Theory[M].Volume 83 of Appl Math Sci.New York:Springer-Verlag,1989.
[3]	Gidas B,NI Wei-min,Nirenberg L.Symmetry and related properties via the maximum principle[J].Commun Math Phys,1979,68(1):209-243. doi: 10.1007/BF01221125
[4]	Joseph D D,Lundgren T S.Quasilinear Dirichlet problems driven by positive sources [J].Arch Rat Mech Anal,1973,49(2):241-269.
[5]	Cac N P,Fink A M,Gupta J A.Nonnegative solutions of quasilinear elliptic problems with nonnegative coefficients[J].J Math Anal Appl,1997,206(1):1-9. doi: 10.1006/jmaa.1997.4882
[6]	Korman P.Solution curves for semilinear equations on a ball[J].Proc Amer Math Soc,1997,125(11):1997-2006. doi: 10.1090/S0002-9939-97-04119-1
[7]	Korman P.Curves of sign-changing solutions for semilinear equations[J].Nonlinear Anal TMA,2002,51(5):801-820. doi: 10.1016/S0362-546X(01)00863-X
[8]	Hai D D.Uniqueness of positive solutions for a class of semilinear elliptic systems [J].Nonlinear Anal TMA,2003,52(4):595-603. doi: 10.1016/S0362-546X(02)00125-6
[9]	姚庆六.单位球上一类非线性Dirichlet问题的正对径解[J].厦门大学学报,自然科学版,2003,42(5):567-569.
[10]	姚庆六.一类奇异二阶拟线性方程的解和正解[J].华东理工大学学报,2007,33(2):290-293.
[11]	姚庆六.一类非线性Dirichlet边值问题正径向解[J].数学物理学报,A辑,2009,29(1):48-56.
[12]	YAO Qing-liu.An iterative method to a class of qualinear boundary value problems[J].J Compu Appl Math,2009,230(1):306-311. doi: 10.1016/j.cam.2008.11.015
[13]	姚庆六.一类奇异二阶边值问题的正周期解[J].数学学报,2007,50(6):1357-1364.
[14]	YAO Qing-liu.Positive solution to a special singular second-order boundary value problem[J].Math Comput Modeling,2008,47(11/12):1284-1291. doi: 10.1016/j.mcm.2007.08.003
[15]	YAO Qing-liu.Existence and multiplicity of positive solutions to a singular elastic beam equation rigidly fixed at both ends[J].Nonlinear Anal TMA,2008,69(8):2683-2694. doi: 10.1016/j.na.2007.08.043
[16]	程其骧,张奠宙,魏国强,等.实变函数与泛函分析基础[M].第二版.北京:高等教育出版社,2003.