Existence of solutions for singular double phase problems via the Nehari manifold method

被引：22

作者：

Liu, Wulong ^{[1
]}

Dai, Guowei ^{[2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

Winkert, Patrick ^{[4
]}

机构：

[1] Yantai Univ, Sch Math & Informat Sci, Yantai 264005, Shandong, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

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

[4] Tech Univ Berlin, Inst Math, Str 17 Juni 136, D-10623 Berlin, Germany

来源：

ANALYSIS AND MATHEMATICAL PHYSICS | 2022年 / 12卷 / 03期

关键词：

Double phase operator; Fibering method; Multiple solutions; Nehari manifold; Singular problems; REGULARITY; MULTIPLICITY; EIGENVALUES; FUNCTIONALS; MINIMIZERS; CALCULUS; ROBIN;

D O I：

10.1007/s13324-022-00686-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we study quasilinear elliptic equations driven by the double phase operator and a right-hand side which has the combined effect of a singular and of a parametric term. Based on the fibering method by using the Nehari manifold we are going to prove the existence of at least two weak solutions for such problems when the parameter is sufficiently small.

引用

页数：25

共 63 条

[1] Multiplicity of negative-energy solutions for singular-superlinear Schrodinger equations with indefinite-sign potential [J].

Alves, Ricardo Lima ;

Santos, Carlos Alberto ;

Silva, Kaye .

COMMUNICATIONS IN CONTEMPORARY MATHEMATICS, 2022, 24 (10)

[2]

[Anonymous], 2012, Homogenization of differential operators and integral functionals

[3] Double phase problems with variable growth and convection for the Baouendi-Grushin operator [J].

Bahrouni, Anouar ;

Radulescu, Vicentiu D. ;

Winkert, Patrick .

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2020, 71 (06)

[4] Elliptic problems with convection terms in Orlicz spaces [J].

Barletta, Giuseppina ;

Tornatore, Elisabetta .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2021, 495 (02)

[5] NON-AUTONOMOUS FUNCTIONALS, BORDERLINE CASES AND RELATED FUNCTION CLASSES [J].

Baroni, P. ;

Colombo, M. ;

Mingione, G. .

ST PETERSBURG MATHEMATICAL JOURNAL, 2016, 27 (03) :347-379

[6] Regularity for general functionals with double phase [J].

Baroni, Paolo ;

Colombo, Maria ;

Mingione, Giuseppe .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2018, 57 (02)

[7] Harnack inequalities for double phase functionals [J].

Baroni, Paolo ;

Colombo, Maria ;

Mingione, Giuseppe .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2015, 121 :206-222

[8] Borderline gradient continuity of minima [J].

Baroni, Paolo ;

Kuusi, Tuomo ;

Mingione, Giuseppe .

JOURNAL OF FIXED POINT THEORY AND APPLICATIONS, 2014, 15 (02) :537-575

[9] Symmetry and monotonicity of singular solutions of double phase problems [J].

Biagi, Stefano ;

Esposito, Francesco ;

Vecchi, Eugenio .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 280 :435-463

[10] REGULARITY RESULTS FOR GENERALIZED DOUBLE PHASE FUNCTIONALS [J].

Byun, Sun-Sig ;

Oh, Jehan .

ANALYSIS & PDE, 2020, 13 (05) :1269-1300

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