THIRD-ORDER NONLINEAR SINGULARLY PERTURBED BOUNDARY VALUE PROBLEM  

作　　者：WANG Guo-can(王国灿) JIN Li(金丽) 

机构地区：[1]Department of Basic Science and Engineering, Dalian Railway Institute, Dalian 116028, P R China Department of Basic Science and Engineering, Dalian Railway Institute, Dalian 116028, P R China

出　　处：《Applied Mathematics and Mechanics(English Edition)》2002年第6期670-677,共8页应用数学和力学（英文版）

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.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.

关 键 词：third order boundary value problem upper and lower solutions Volterra type integral operator existence and asymptotic estimates 

分 类 号：O175.8[理学—数学]