一类退化椭圆方程解的存在性与爆破行为  

Existence and blow-up behavior of solutions for a class of degenerate elliptic equations

作　　者：刘航 田书英 LIU Hang;TIAN Shuying(Department of Mathematics,School of Science,Wuhan University of Technology,Wuhan 430070,China)

机构地区：[1]武汉理工大学理学院数学系,湖北武汉430070

出　　处：《浙江大学学报（理学版）》2024年第3期282-291,共10页Journal of Zhejiang University（Science Edition）

基　　金：国家自然科学基金资助项目(12071364).

摘　　要：研究了一类具有位势函数的锥形退化椭圆方程。通过探究约束极小化问题,建立了方程基态解的存在性定理,并分析了其爆破行为。证明了当参数满足一定条件时,约束极小化问题至少存在1个可达元,但当参数不满足此条件时,不存在可达元。详细分析了当参数趋近于临界值时,可达元的爆破行为。A class of conical degenerate elliptic equations with potential functions is studied.The existence of the ground state solution for the equation is established by studying the constrained minimization problem.The blow-up behavior is analyzed as well.Specifically,we prove that there exists at least one minimizer for the constraint minimization problem under certain conditions,but the minimizer does not exist when these conditions are unsatisfied.The blow-up behavior of the minimizer is analyzed in detail when the parameter approaches the critical value.

关 键 词：退化椭圆方程 约束极小化问题 基态解 

分 类 号：O176.3[理学—数学]