一般区域上含跳跃项平均曲率算子方程解的全局分歧OA北大核心CSTPCD
Bifurcation of solutions for the problems involving jumping non-linearities with mean curvature operator on general domain
建立了一般区域上含跳跃项平均曲率算子方程解的全局分歧定理,研究了问题{-div(▽u/√1-|▽u|2)=α(x)u++β(x)u-+λa(x)f(u),x∈Ω,u=0,x∈∂Ω解的存在性,其中λ≠0为实参数,Ω为在RN中有界且在其边界上光滑的C2区域,N≥1,a∈C((Ω),(0,∞)),u+=max{u,0},u-=min{-u,0},α,β∈C((Ω));f∈C(R,R),对于s≠0,满足sf(s)>0;f0∈[0,∞],其中f0=lim|s|→0 f(s)/s.
In this paper,we firstly establish an global bifurcation result for the problems involving jumping non-linearities with mean curvature operator in Minkowski space.As applications of the above results,we study the existence of solutions for the following problem{-div(▽u/√1-|▽u|2)=α(x)u++β(x)u-+λa(x)f(u),x∈Ω,u=0,x∈∂Ω,where λ≠0 is a real parameter,Ω is a general C2 bounded domain in RN with a smooth boundary ∂Ω and N≥1,a∈C((Ω),(0,∞)),u+=max{u,0},u-=min{-u,0},α,β∈C((Ω));f∈C(R,R),sf(s)>0 for s≠0,and f0∈[0,∞],where f0=lim|s|→0 f(s)/s.
沈文国
广东科技学院 通识教育学院,广东 东莞 523083
数学
平均曲率算子含跳跃非线性项问题解的全局分歧
mean curvature operatorthe problems involving jumping non-linearitiesglobal bifurcation of solutions
《浙江大学学报（理学版）》 2024 (004)
443-449 / 7
国家自然科学基金资助项目(11561038).
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