探究摄动具有双参数拟线性微分方程奇摄动Robin边值不足(英文)
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AbstractIn this paper， a class of singularly perturbed Robin boundary value problems of quasilinear differential equation with two parameters is studied. Using the method of differential inequalities， the structure of solutions for the problems is discussed in three different cases about two all parameters. In addition， the asymptotic solutions he been found and the remainder term are given as well.
Key wordsSingular perturbation； Two parameters； Differential inequalities； Robin problem
CLC numberO 17
There are a mass of singularly perturbed problems with two all parameters in many areas， studying this kind of singularly perturbed problems is a very focused object in international academic circles. Recently， many approximate methods he been developed and refined， including the method of differential inequalities. There he been a lot of works in thiield[1？6]， but they were mostly within thefield of singularly perturbed problems with one parameter， and there are a few of results is produced. In this paper， using the method of differential inequalities， we study a class of Robin boundary value problems for nonlinear second order differential equation with two all parameters.
Wefirst consider the boundary value problem （1）-（2）. We he the following hypotheses：
[H1]For the reduced equation g（t，u） = 0， there exists a solution u（t）∈C2[a，b]，such that u′′（t）≥0，u′f≥0，u（a）？p1u′（a）≤A，u（b）≤B.
[H2]f（t，y），g（t，y），gy（t，y）∈C（D0（u）），where D0（u） ：= {（t，y）|a≤t≤b，0≤y？u（t）≤d（t）}，and d（t） > 0 is a continuous function such that
K W Chang and F A Howes. Nonlinear Singular Perturbation Phenomena： Theory And Applications[M]. New York： Springer-verlag， 1984.
O’malley R E. In源于：论文封面格式www.618jyw.com
troduction to Singular Perturbation[M]. New York： Academic Press， 1974.
[3] Nayfeh A H. Introduction to Perturbation Techniques[M]. New York： John， 1981.
[4] Jager E M De， Jiang F. The Theory of Singular Perturbation[M]. Amsterdam： Publishing Corporation， 1996.
[5] Liu Shude， Lu Shiping， Yao Jingsun， Chen Huai-jun. Singular Perturbation Boundary And Corner Layer Theory[M]. Beijing： Science Press，2012.
[6] Zhou Mingru， Du Zengji， Wang Guangwa. The Theory Of Differential Inequality In Singular Perturbation[M]. Beijing： Science Press， 2012.
[7] Mo Jiaqi. Singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters[J]. Chinese Annals of Mathematics， 2010， 33A（1）： 331-336.
[8] Mo Jiaqi， Liu Shude. Singularly perturbed solution for semilinear reaction diffusion equations with two parameters[J]. Applied Mathematics and Mechanics， 2009， 30（5）： 607-612.
[9] Mo Jiaqi， Yao Jingsun. A class of Singularly perturbed nonlinear reaction diffusion equations with two parameters[J]. J Math， 2011， 33（2） ： 341-346.
[10] Zhang Hanlin. The corner solution for quasilinear differential equation with two parameters[J]. Applied Mathematics and Mechanics， 1997， 18（5）： 503-510.
[11] Heidel J W. A second-order nonlinear boundary value problem[J]. Journal of Mathematical Analysis and Applications， 1974， 48： 493-503.
Key wordsSingular perturbation； Two parameters； Differential inequalities； Robin problem
CLC numberO 17
5.14Document codeA
1IntroductionThere are a mass of singularly perturbed problems with two all parameters in many areas， studying this kind of singularly perturbed problems is a very focused object in international academic circles. Recently， many approximate methods he been developed and refined， including the method of differential inequalities. There he been a lot of works in thiield[1？6]， but they were mostly within thefield of singularly perturbed problems with one parameter， and there are a few of results is produced. In this paper， using the method of differential inequalities， we study a class of Robin boundary value problems for nonlinear second order differential equation with two all parameters.
Wefirst consider the boundary value problem （1）-（2）. We he the following hypotheses：
[H1]For the reduced equation g（t，u） = 0， there exists a solution u（t）∈C2[a，b]，such that u′′（t）≥0，u′f≥0，u（a）？p1u′（a）≤A，u（b）≤B.
[H2]f（t，y），g（t，y），gy（t，y）∈C（D0（u）），where D0（u） ：= {（t，y）|a≤t≤b，0≤y？u（t）≤d（t）}，and d（t） > 0 is a continuous function such that
K W Chang and F A Howes. Nonlinear Singular Perturbation Phenomena： Theory And Applications[M]. New York： Springer-verlag， 1984.
O’malley R E. In源于：论文封面格式www.618jyw.com
troduction to Singular Perturbation[M]. New York： Academic Press， 1974.
[3] Nayfeh A H. Introduction to Perturbation Techniques[M]. New York： John， 1981.
[4] Jager E M De， Jiang F. The Theory of Singular Perturbation[M]. Amsterdam： Publishing Corporation， 1996.
[5] Liu Shude， Lu Shiping， Yao Jingsun， Chen Huai-jun. Singular Perturbation Boundary And Corner Layer Theory[M]. Beijing： Science Press，2012.
[6] Zhou Mingru， Du Zengji， Wang Guangwa. The Theory Of Differential Inequality In Singular Perturbation[M]. Beijing： Science Press， 2012.
[7] Mo Jiaqi. Singularly perturbed asymptotic solutions for higher order semilinear elliptic equations with two parameters[J]. Chinese Annals of Mathematics， 2010， 33A（1）： 331-336.
[8] Mo Jiaqi， Liu Shude. Singularly perturbed solution for semilinear reaction diffusion equations with two parameters[J]. Applied Mathematics and Mechanics， 2009， 30（5）： 607-612.
[9] Mo Jiaqi， Yao Jingsun. A class of Singularly perturbed nonlinear reaction diffusion equations with two parameters[J]. J Math， 2011， 33（2） ： 341-346.
[10] Zhang Hanlin. The corner solution for quasilinear differential equation with two parameters[J]. Applied Mathematics and Mechanics， 1997， 18（5）： 503-510.
[11] Heidel J W. A second-order nonlinear boundary value problem[J]. Journal of Mathematical Analysis and Applications， 1974， 48： 493-503.
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