非线性项在零点和无穷远处非渐进增长的高维变权p-Laplacian问题径向结点解的存在性  

The existence of radial nodal solutions for the high-dimensional sign-changing weight p-Laplacian with non-asymptotic nonlinearity at 0 and ∞

作　　者：沈文国 包理群[2] SHEN Wenguo;BAO Liqun(Department of Basic Courses,Lanzhou Institute of Technology,Lanzhou 730050,China;Department of Electronic and Information Engineering,Lanzhou Institute of Technology,Lanzhou 730050,China)

机构地区：[1]兰州工业学院基础学科部,兰州730050 [2]兰州工业学院电子信息工程系,兰州730050

出　　处：《华中师范大学学报（自然科学版）》2022年第4期561-566,共6页Journal of Central China Normal University：Natural Sciences

基　　金：兰州工业学院‘开物’科研创新团队支持计划项目(2018KW-03);国家自然科学基金项目(11561038);甘肃省自然科学基金项目(20JR5RA377)。

摘　　要：该文研究问题-div(φ_(p)(▽u))=γm(x)f(u),x∈B,u(x)=0,x∈∂B径向结点解的存在性.其中B是R^(N)上的一个单位球,N≥2,1<p<+∞,φ_(p)(s)=|s|^(p-2) s,m∈M(B)是变号函数且M(B)=m∈C(■)是径向对称的且|meas{x∈B,m(x)>0}≠0.γ是一个参数,f∈C(ℝ,ℝ),对于s≠0满足sf(s)>0.首先,当满足f_(0),f_(∞)∈(0,∞)时,引出上述问题的全局分歧结论;其次,给出序列集取极限的引理;再次,当满足f_(0)■(0,∞)或f_(∞)■(0,∞),且γ≠0满足一定区间时,利用上述全局分歧技巧和连通序列集取极限的方法,可以获得上述问题径向结点解的存在性,其中f_(0)=lim/|s|→0 f(s)/φ_(p)(s),f_(∞)=lim/|s|→∞f(s)/φ_(p)(s).In this paper,the existence of radial nodal solutions for the following p-Laplacian problem-div(φ_(p)(▽u))=γm(x)f(u),x∈B,u(x)=0,x∈∂B is studied,where B is the unit open ball of and N≥2,0<p<+∞,φ_(p)(s)=|s|^(p-2) s,m∈M(B)is a sign changing function with M(B)=m∈C(■)is radially symmetric||meas{x∈B,m(x)>0}≠0.γis a parameter,f∈C(ℝ,ℝ),sf(s)>0 for s≠0.Firstly,the bifurcation result of the above problem if f_(0)∈(0,∞)or f_(∞)∈(0,∞)is obtained;Secondly,the approximation of connected components is obtained;Finally,if f_(0)■(0,∞)or f_(∞)■(0,∞)and the parameterγ≠0 satisfies the intervals,where f_(0)=lim_(|s|→0 f)(s)/φ_(p)(s),f_(∞)=lim_(|s|→∞)f(s)/φ_(p)(s),using unilateral global bifurcation techniques and the approximation of connected components,our main results are proved.

关 键 词：单侧全局分歧 高维变权p-Laplacian问题 径向结点解 非线性项在零点和无穷远处非渐进增长 

分 类 号：O175.8[理学—数学]