POSITIVE SOLUTIONS FOR NONLINEAR SINGULAR PROBLEMS WITH SIGN-CHANGING NONLINEARITIES

被引：1

作者：

Bai, Yunru ^{[1
]}

Papageorgiou, Nikolaos S. ^{[2
]}

Zeng, Shengda ^{[3
,4
,5
,6
]}

机构：

[1] Guangxi Univ Sci & Technol, Sch Sci, Liuzhou 545006, Guangxi, Peoples R China

[2] Natl Tech Univ Athens, Dept Math, Zograrou Compus, Athens 15780, Greece

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

[4] Yulin Normal Univ, Guangxi Coll & Univ Key Lab Complex Syst Optimizat, Yulin 537000, Guangxi, Peoples R China

[5] Nanjing Univ, Dept Math, Nanjing 210093, Jiangsu, Peoples R China

[6] Fac Math & Comp Sci, Ul Lojasiewicza 6, PL-30348 Krakow, Poland

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2023年 / 16卷 / 11期

基金：

欧盟地平线“2020”; 中国博士后科学基金;

关键词：

Nonlinear regularity; nonlinear maximum principle; Hardy's inequality; singular term; superlinear perturbation; EQUATIONS;

D O I：

10.3934/dcdss.2023131

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

. We consider a Dirichlet problem driven by a general nonlinear, nonhomogeneous differential operator. The reaction has the competing effects of a singular term and of a parametric perturbation which is superlinear and sign-changing. Using variational tools from critical point theory together with truncation and comparison techniques, we show that for all small values of the parameter, the problem has at least two positive smooth solutions. Also, we show the existence of a smallest positive solution (minimal positive solution).

引用

页码：2945 / 2963

页数：19

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