THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

Applied Mathematics and Mechanics (English Edition) ›› 2002, Vol. 23 ›› Issue (6): 670-677.

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

王国灿, 金丽

Department of Basic Science and Engineering, Dalian Railway Institute, Dalian 116028, P. R. China

收稿日期:2000-03-21 修回日期:2001-12-26 出版日期:2002-06-18 发布日期:2002-06-18

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

WANG Guo-can, JIN Li

Department of Basic Science and Engineering, Dalian Railway Institute, Dalian 116028, P. R. China

Received:2000-03-21 Revised:2001-12-26 Online:2002-06-18 Published:2002-06-18

摘要/Abstract

摘要： Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

Abstract: Third order singulary perturbed boundary value problem by means of differential inequality theories is studied. Based on the given results of second order nonlinear boundary value problem, the upper and lower solutions method of third order nonlinear boundary value problems by making use of Volterra type integral operator was established. Specific upper and lower solutions were constructed, and existence and asymptotic estimates of solutions under suitable conditions were obtained. The result shows that it seems to be new to apply these techniques to solving these kinds of third order singularly perturbed boundary value problem. An example is given to demonstrate the applications.

中图分类号:

O175.8

王国灿;金丽. THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 670-677.

WANG Guo-can;JIN Li. THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM[J]. Applied Mathematics and Mechanics (English Edition), 2002, 23(6): 670-677.

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THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM

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