一类半线性椭圆型Neumann边值问题解的存在唯一性  

Existence and Uniqueness of Solutions to a Class of Neumann Problems for the Semilinear Elliptic Equation

作　　者：邢慧 陈红斌[2] 

机构地区：[1]西安工程大学理学院,西安710048 [2]西安交通大学数学与统计学院,西安710049

出　　处：《工程数学学报》2017年第6期622-628,共7页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11626182);西安工程大学博士科研启动基金(BS1433)~~

摘　　要：半线性椭圆型方程解的性质蕴含了方程的丰富信息,对于描述各种现象的发展规律起着至关重要的作用.多物种互助模型的平衡解以及经济均衡点的存在性问题等都可以转化为Neumann边值问题解的存在性.本文研究一类半线性椭圆型方程Neumann边值问题解的存在唯一性.在假定非线性项满足渐近非一致条件的情况下,我们利用拓扑度理论和特征值比较原理得到了解的存在性,运用特征值比较原理证明了解的唯一性.推广和补充了以往的相关研究成果.作为应用,文中通过一个例子验证了所得结论.The solutions to semilinear elliptic partial differential equations contain rich information about the equations, which is very important for describing the development of various phenomena. The existence of equilibrium solutions of multi-species mutual aid model and the economic equilibrium point can be transformed into the existence of the solutions to Neumann boundary value problems. In this paper, we study the existence and uniqueness of the solutions for a class of semilinear elliptic equations with Neumann boundary value conditions. Using the topological degree theory and the eigenvalue comparison principle, we obtain the existence of the solutions under the assumption that the nonlinear terms satisfy the asymptotic nonuniform conditions. Using the eigenvalue comparison principle, we prove the uniqueness of the solutions.The obtained results extend and complement some relevant existing works. As an application,an example is given to verify the obtained results.

关 键 词：NEUMANN边值问题 解的存在唯一性 渐近非一致条件 拓扑度理论 特征值比较原理 

分 类 号：O175.2[理学—数学]