一类超线性双调和方程正解的存在性  

Existence of positive solution for a class of superlinear biharmonic equations

作　　者：吉蕾[1] JI Lei(Department of Mathematics,Jinzhong University,Jinzhong 030619,China)

机构地区：[1]晋中学院数学系,山西晋中030619

出　　处：《安徽大学学报（自然科学版）》2024年第5期12-17,共6页Journal of Anhui University(Natural Science Edition)

基　　金：山西省高等学校科技创新项目(2021L493);山西省高等学校教学改革创新项目(J2021620)。

摘　　要：研究以下双调和方程{Δ^(2)u+cΔu=f(x,u),x∈Ω,Δu=u=0,x∈∂Ω,其中Ω∈R^(N)是有界开集,其边界∂Ω光滑.c∈R,f:Ω×R→R是Caratheodory函数.当非线性项f(x,u)在无穷远处为超线性时,通过山路引理和强极大值原理获得了该方程的正解,所设条件弱于相关文献中的条件,使得非线性项更具一般性,从而推广了相关文献中关于超线性的结果.This paper studied the following biharmonic equation{Δ^(2)u+cΔu=f(x,u),x∈Ω,Δu=u=0,x∈∂Ω,whereΩ×R^(N) was an open bounded set,with smooth boundaries.c∈R,f:Ω×R→R was a Caratheodory function.When the nonlinearity f(x,u)was superlinear at infinity,using the mountain pass lemma and strong maximum principle,we obtained the existence of positive solution for the equation.The conditions set were weaker than those in other reference,which made the nonlinearity more general,thus the conclusion generalized the results on superlinearity in other reference.

关 键 词：双调和 超线性 变分方法 正解 

分 类 号：O156[理学—数学]