一维有界区域上双稳态方程多重正解的存在性  

Existence of multiple positive solutions for bistable equations in one-dimensional bounded domains

作　　者：金怡 凌慧铧 陆俊帆 JIN Yi;LING Huihua;LU Junfan(Mathematics and Science College,Shanghai Normal University,Shanghai 200234,China)

机构地区：[1]上海师范大学数理学院,上海200234

出　　处：《上海师范大学学报（自然科学版）》2022年第3期294-300,共7页Journal of Shanghai Normal University(Natural Sciences)

基　　金：国家自然科学基金(12071299)。

摘　　要：研究了一维有界区域上双稳态反应扩散方程的正平衡解.构造了一些双稳态非线性项,使用相平面分析和常微分方程理论,证明了相应的方程多个正平衡解的存在性.In this paper,we study the positive stationary solutions of the bistable reaction-diffusion equation in one-dimensional bounded domains.We construct some bistable nonlinear terms,and use phase plane analysis and the theory of ordinary differential equation to prove the existence of multiple positive stationary solutions of the corresponding equation.

关 键 词：反应扩散方程 双稳态方程 平衡解 多重正解 

分 类 号：O175.25[理学—数学]