含一阶导数项的二阶常微分方程Dirichlet边值问题解的存在唯一性  

Existence and uniqueness of solutions to Dirichlet boundary value problems for second-order ordinary differential equation with first-order derivative terms

作　　者：陈慧玲 崔玉军 CHEN Huiling;CUI Yujun(College of Mathematics and Systems Science,Shandong University of Science and Technology,Qingdao,Shandong 266590,China)

机构地区：[1]山东科技大学数学与系统科学学院,山东青岛266590

出　　处：《山东科技大学学报（自然科学版）》2020年第6期109-114,共6页Journal of Shandong University of Science and Technology(Natural Science)

基　　金：国家自然科学基金项目(11371221,11571207);山东省自然科学基金项目(ZR2018MA011)。

摘　　要：为了研究二阶常微分方程Dirichlet边值问题解的存在唯一性,考虑到非线性项函数中含有未知函数的一阶导数,首先证明求解含一阶导数项的二阶常微分方程Dirichlet边值问题等价于求积分方程组的连续解,然后在广义的李普希茨条件下运用Picard逐次逼近法和矩阵的谱理论给出积分方程组连续解的存在唯一性结论。To study the existence and uniqueness of the solutions to Dirichlet boundary value problems for second-order ordinary differential equations and considering that the nonlinear term contains first-order derivatives of unknown functions,this study initially proves that the solutions to Dirichlet boundary value problems for second-order differential equations with first-order derivative terms was equivalent to the continuous solution to integral equation set.Subsequently,the existence and uniqueness of the continuous solution of integral equation set under the generalized Lipshitz condition is proved by using Picard successive approximation method and spectral theory of matrices.

关 键 词：微分方程 边值问题 逐次逼近法 存在唯一性 

分 类 号：O17[理学—数学]