The existence of radial nodal solutions for the high-dimensional sign-changing weight p-Laplacian with non-asymptotic nonlinearity at 0 and ∞
SHEN Wenguo1， BAO Liqun2
(1.Department of Basic Courses， Lanzhou Institute of Technology， Lanzhou 730050， China；2.Department of Electronic and Information Engineering， Lanzhou Institute of Technology， Lanzhou 730050， China)
Abstract：In this paper， the existence of radial nodal solutions for the following p-Laplacian problem－div(φp(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〈＋∞， φp(s)＝|s|p－2s， m∈M(B) is a sign changing function with M(B)＝－(B)is radially symmetric|.γ is a parameter， f∈C(，)， sf(s)〉0 for s≠0. Firstly， the bifurcation result of the above problem if f0∈(0，∞) or f∞∈(0，∞) is obtained； Secondly， the approximation of connected components is obtained ；Finally， if f0(0，∞) or f∞(0，∞) and the parameter γ≠0 satisfies the intervals， where f0＝lim|s|→0f(s)/φp(s)，f∞＝lim|s|→∞f(s)/φp(s)，using unilateral global bifurcation techniques and the approximation of connected components， our main results are proved.
沈文国,包理群. 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[J]. 华中师范大学学报(自然科学版), 2022, 56(4): 561-566.
SHEN Wenguo,BAO Liqun. The existence of radial nodal solutions for the high-dimensional sign-changing weight p-Laplacian with non-asymptotic nonlinearity at 0 and ∞. journal1, 2022, 56(4): 561-566.
2022, Vol. 56 
