一类四阶半线性方程的奇摄动解

莫嘉奇

doi:10.3879/j.issn.1000-0887.2009.11.011

一类四阶半线性方程的奇摄动解

doi: 10.3879/j.issn.1000-0887.2009.11.011

莫嘉奇^1,2

安徽师范大学数学系,安徽芜湖 241000;2.上海高校计算科学研究院SJTU研究所,上海 200240

基金项目: 国家自然科学基金资助项目(40676016;40876010);中国科学院知识创新工程重要方向资助项目(KZCX2-YW-Q03-08);LASG国家重点实验室专项经费资助项目;上海市教育委员会E-研究院建设计划项目(E03004)资助课题

详细信息

中图分类号: O175.14
计量
- 文章访问数: 1644
- HTML全文浏览量: 82
- PDF下载量: 780
- 被引次数: 0
出版历程
- 收稿日期: 2009-07-03
- 修回日期: 2009-09-17
- 刊出日期: 2009-11-15

On a Class of Singular Perturbation Solution for Semilinear Equtions of Fourth Order

MO Jia-qi^1,2

Department of Mathematics, Anhui Normal University, Wuhu, Aahui 241000, P. R. China;

摘要

摘要: 讨论了一类四阶半线性方程奇摄动边值问题．利用上下解方法，研究了边值问题解的存在性和渐近性态．指出了在该文的情形下具有两参数的原奇摄动问题的解只有一个边界层
- 半线性 /
- 两参数 /
- 奇摄动 /
- 上下解
Abstract: A class of singularly perturbed boundary value problem for semilinear equation of fourth order with two parameters is considered. Under suitable conditions, using lower and upper solutions method, the existence and asymptotic behavior of solution for boundary value problem were studied. It is pointed out that the solution for original singularly perturbed problem with two parameters has only one boundary layer.
- semilinear /
- two parameters /
- singular perturbation /
- lower and upper solutions

HTML全文

参考文献(19)

[1]	Guarguaglini F R,Natalini R.Fast reaction limit and large time behavior of solutions to a nonlinear model of sulphation phenomena[J].Commun Partial Diff Equs,2007,32(2):163-189. doi: 10.1080/03605300500361438
[2]	Hovhannisyan G,Vulanovic R.Stability inequalities for one-dimensional singular perturbation problems[J].Nonlinear Stud,2008,15(4):297-322.
[3]	Abid I,Jieli M,Trabelsi N.Weak solutions of quasilinear biharmonic problems with positive,increasing and convex nonlinearities[J].Anal Appl Singap,2008,6(3):213-227. doi: 10.1142/S0219530508001134
[4]	Graef J R,Kong L.Solutions of second order multi-point boundary value problems[J].Math Proc Camb Philos Soc,2008,145(2):489-510.
[5]	Barbu L,Cosma E.Elliptic regularizations for the nonlinear heat equation[J].J Math Anal Appl,2009,351(2):392-399. doi: 10.1016/j.jmaa.2008.10.033
[6]	MO Jia-qi.A singularly perturbed nonlinear boundary value problem[J].J Math Anal Appl,1993,178(1):289-293. doi: 10.1006/jmaa.1993.1307
[7]	MO Jia-qi.Singular perturbation for a class of nonlinear reaction diffusion systems[J].Science in China,Ser A, 1989,32(11):1306-1315.
[8]	MO Jia-qi.A class of singularly perturbed differential-difference reaction diffusion equations[J].Adv Math,2009,38(2):227-230.
[9]	MO Jia-qi,LIN Wan-tao.Asymptotic solution of activator inhibitor systems for nonlinear reaction diffusion equations[J].J Sys Sci Complexity,2008,20(1):119-128.
[10]	MO Jia-qi,WANG Hui.Nonlinear singularly perturbed approximate solution for generalized Lotke-Volterra ecological model[J].Acta Ecologica Sinica,2007,27(10):4366-4370.
[11]	MO Jia-qi,ZHU Jiang,WANG Hui.Asymptotic behavior of the shock solution for a class of nonlinear equations[J].Progress in Natural Sci,2003,13(9):768-770. doi: 10.1080/10020070312331344400
[12]	MO Jia-qi.Approximate solution of homotopic mapping to solitary for generalized nonlinear KdV system[J].Chin Phys Lett,2009,26(1):010204-1-010204-4. doi: 10.1088/0256-307X/26/1/010204
[13]	MO Jia-qi.A variational iteration solving method for a class of generalized Boussinesq equations[J].Chin Phys Lett,2009,26(6):060202-1-060202-3. doi: 10.1088/0256-307X/26/6/060202
[14]	MO Jia-qi.Homotopic mapping solving method for gain fluency of laser pulse amplifier[J].Science in China,Ser G,2009,39(5):568-661.
[15]	MO Jia-qi,LIN Wan-tao,WANG Hui.Variational iteration solving method of a sea-air oscillator model for the ENSO[J].Prog Nat Sci,2007,17(2):230-232. doi: 10.1080/10020070612331343252
[16]	MO Jia-qi.A class of homotopic solving method for ENSO model[J].Acta Math Sci，2009,29(1):101-109.
[17]	de Jager E M,Jiang F R.The Theory of Singular Perturbation[M].Amsterdam:North- Holland Publishing Co,1996.
[18]	Howes F A.Differential inequalities and applications to nonlinear singular perturbation problems[J].J Differential Equations,1976,20(1):133-149. doi: 10.1016/0022-0396(76)90100-5
[19]	CHEN Li-hua,MO Jia-qi,LIU Shu-de.The singularly perturbed solution for nonlinear equations of fourth order with two parameters[J].J Shanghai Jiaotong Univ,2008,E-13,(4):509-512.