一类半线性椭圆型方程Dirichlet问题解的存在性  

Existence of Solutions to Dirichlet Problem for a Class of Semilinear Elliptic Equations

作　　者：周冉[1] 韦玉程[2] ZHOU Ran;WEI Yucheng(College of Mathematics,Jilin University,Changchun 130012,China;School of Mathematics and Physics,Hechi University,Yizhou 546300,Guangxi Zhuang Autonomous Region,China)

机构地区：[1]吉林大学数学学院,长春130012 [2]河池学院数理学院,广西宜州546300

出　　处：《吉林大学学报（理学版）》2022年第6期1217-1223,共7页Journal of Jilin University:Science Edition

基　　金：广西自然科学基金(批准号:2018GXNSFAA281307);广西教育厅高等教育本科教学改革工程项目(批准号:2020JGZ145);河池学院高层次人才科研启动项目(批准号:2021GCC025);吉林省教育厅科学研究规划项目(批准号:JJKH20200934KJ)。

摘　　要：利用上下解方法讨论一类具有超临界增长非线性项的椭圆方程,先证明Dirichlet问题在限制区域内解的存在性,再结合新的变分原理,证明限制区域内的局部解可延展到全区域.By using the method of upper and lower solutions, we discussed a class of elliptic equations with nonlinear terms of supercritical growth. We first proved the existence of solutions of the Dirichlet problem in the restricted region, and then proved that the local solutions in the restricted region could be extended to the whole region by combining a new variational principle.

关 键 词：超临界增长 变分法 上下解 Carathéodory函数 

分 类 号：O175.25[理学—数学]