A Positive Solution for a Weighted p-Laplace Equation with Hardy-Sobolev's Critical Exponent

被引：1

作者：

Razani, Abdolrahman ^{[1
]}

Costa, Gustavo S. ^{[2
]}

Figueiredo, Giovany M. ^{[3
]}

机构：

[1] Imam Khomeini Int Univ, Dept Pure Math, Fac Sci, Qazvin 3414896818, Iran

[2] Univ Fed Maranhao, Dept Matemat, CCET, BR-65080805 Sao Luis, MA, Brazil

[3] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY | 2024年 / 47卷 / 02期

关键词：

Subcritical growth; Critical exponent; Caffarelli-Kohn-Nirenberg inequality; Laplace operator; Degenerate elliptic problem; ELLIPTIC-EQUATIONS; EXISTENCE; INEQUALITIES;

D O I：

10.1007/s40840-024-01657-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Here, considering-infinity <a<N-pp,a <= e <= a+1,d=1+a-eandp & lowast;:= p & lowast;(a,e)=Np/N-dp, the existence of positive solution of a weighted p-Laplace equation involving vanishing potentials -Delta(ap)u+V(x)|x|-(ep & lowast;)|u|(p-2)u=|x(|-ep & lowast;)f(u) in R(N)is proved, where the potential V can vanish at infinity with exponential decayandfis a function with subcritical growth of classC1.We use Del Pino & Felmer's arguments to overcome the lack of compactness and the Moser iteration method with Caffarelli-Kohn-Nirenberg inequality to obtain estimates of the solution in L infinity(R-N).

引用

页数：22

共 25 条

[1] Existence of solutions for a class of elliptic equations in RN with vanishing potentials [J].