Singular elliptic problems with unbalanced growth and critical exponent

被引：23

作者：

Kumar, Deepak ^{[1
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
]}

Sreenadh, K. ^{[1
]}

机构：

[1] Indian Inst Technol Delhi, Dept Math, Hauz Khaz, New Delhi 110016, India

[2] AGH Univ Sci & Technol, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[3] Univ Craiova, Dept Math, Craiova 200585, Romania

[4] Univ Elect Sci & Technol China, Sch Math Sci, Chengdu 611731, Sichuan, Peoples R China

来源：

NONLINEARITY | 2020年 / 33卷 / 07期

关键词：

(p; q)-Laplace equation; double-phase energy; Sobolev critical exponent; singular problem; DOUBLE-PHASE; POSITIVE SOLUTIONS; DIRICHLET PROBLEM; REGULARITY; EXISTENCE; EQUATIONS; CONCAVE; (P; NONLINEARITIES; Q)-LAPLACIAN;

D O I：

10.1088/1361-6544/ab81ed

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we study the existence and multiplicity of solutions of the following (p, q)-Laplace equation with singular nonlinearity: {-Delta(p)u-beta Delta(q)u = lambda u(-delta) + u(r-1), u > 0, in Omega u =0 on partial derivative Omega, where Omega is a bounded domain in R-n with boundary, 1 < q < p < r <= p*, where p* = np/n-p, 0 < delta < 1, n > p and lambda, beta > 0 are parameters. We prove existence, multiplicity and regularity of weak solutions of (P-lambda) for suitable range of lambda. We also prove the global existence result for problem (P-lambda).

引用

页码：3336 / 3369

页数：34

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