Singular anisotropic equations with a sign-changing perturbation

被引：1

作者：

Liu, Zhenhai ^{[1
,2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

机构：

[1] Yulin Normal Univ, Ctr Appl Math Guangxi, Yulin 537000, Peoples R China

[2] Guangxi Minzu Univ, Guangxi Key Lab Univ Optimizat Control & Engn Calc, Nanning 530006, Guangxi, Peoples R China

[3] Natl Tech Univ Athens, Dept Math, Zografou Campus, Athens 15780, Greece

来源：

NONLINEAR ANALYSIS-MODELLING AND CONTROL | 2023年 / 28卷 / 06期

关键词：

variable exponents; modular function; Luxemburg norm; regularity theory; maximum principle; EXISTENCE;

D O I：

10.15388/namc.2023.28.33472

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider an anisotropic Dirichlet problem driven by the variable (p, q)-Laplacian (double phase problem). In the reaction, we have the competing effects of a singular term and of a superlinear perturbation. Contrary to most of the previous papers, we assume that the perturbation changes sign. We prove a multiplicity result producing two positive smooth solutions when the coefficient function in the singular term is small in the L infinity-norm.

引用

页码：1120 / 1137

页数：18

共 17 条

[1] MULTIPLICITY RESULTS FOR NONHOMOGENEOUS ELLIPTIC EQUATIONS WITH SINGULAR NONLINEARITIES [J].

Arora, Rakesh .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2022, 21 (06) :2253-2269

[2]

Byun SS, 2017, CALC VAR PARTIAL DIF, V56, DOI 10.1007/s00526-017-1152-6

[3]

CruzUribe DV, 2013, APPL NUMER HARMON AN, DOI 10.1007/978-3-0348-0548-3

[4] Monotone continuous dependence of solutions of singular quenching parabolic problems [J].

Diaz, Jesus Ildefonso ;

Giacomoni, Jacques .

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2023, 72 (04) :2593-2602

[5] Lebesgue and Sobolev Spaces with Variable Exponents [J].

Diening, Lars ;

Harjulehto, Petteri ;

Hasto, Peter ;

Ruzicka, Michael .

LEBESGUE AND SOBOLEV SPACES WITH VARIABLE EXPONENTS, 2011, 2017 :1-+

[6] Global C1,α regularity for variable exponent elliptic equations in divergence form [J].

Fan, Xianling .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2007, 235 (02) :397-417

[7] Existence of solutions for p(x)-Laplacian Dirichlet problem [J].

Fan, XL ;

Zhang, QH .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2003, 52 (08) :1843-1852

[8] Existence of solutions for a nonlinear problem at resonance [J].

Haddaoui, Mustapha ;

Lebrimchi, Hafid ;

Ouhamou, Brahim ;

Tsouli, Najib .

DEMONSTRATIO MATHEMATICA, 2022, 55 (01) :482-489

[9]

Hu S., 2022, Research Topics in Analysis. Volume I: Grounding Theory, DOI [10.1007/978-3-031-17837-5, DOI 10.1007/978-3-031-17837-5]

[10] Singular elliptic problems with unbalanced growth and critical exponent [J].

Kumar, Deepak ;

Radulescu, Vicentiu D. ;

Sreenadh, K. .

NONLINEARITY, 2020, 33 (07) :3336-3369

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