一类平面上拟线性双调和方程正径向解的存在唯一性  

Uniqueness and Existence of Positive Radial Solutions for a Class of Quasilinear Biharmonic Equations in the Plane

作　　者：卜莹 柏仕坤 BU Ying;BAI Shikun(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331

出　　处：《重庆师范大学学报（自然科学版）》2023年第2期108-112,共5页Journal of Chongqing Normal University:Natural Science

基　　金：国家自然科学基金面上项目(No.11601048);重庆市自然科学基金项目(No.cstc2020jcyj-msxmX0123)。

摘　　要：[目的]研究一类平面上拟线性双调和方程。[方法]首先利用径向对称的方法将该方程转化为常微分方程边值问题,进而得到等价的Hammerstein型积分方程,在合适的工作空间中构建算子方程,借助Green函数的一个不等式和增算子不动点定理获得本文的主要结论。[结果]获得所研究方程正径向解的存在唯一性,且给出了正解的迭代序列。[结论]举例说明所得结论具有较广泛的适应性,所得结果推广和改进了近期已发表的相应结论。[Purposes]Consider a class of quasilinear biharmonic equations in the plane.[Methods]This problem can be transformed into an ordinary differential equation boundary value problem via the method of radial symmetry,and obtained its equivalent Hammerstein-type integral equation.Then,an operator equation is established in an appropriate work space,and using an inequality from the Green and the fixed point theorem of increasing operators,the main results are obtained.[Findings]The uniqueness and existence of positive radial solutions are obtained,and an iterative sequence for the positive solution is also offered.[Conclusions]Two examples are given to illustrate that the conclusion has a wide application,and the result extends and generalizes the existing study in the literature.

关 键 词：拟线性双调和方程 正径向解 增算子不动点定理 迭代 

分 类 号：O175.25[理学—数学]