Constant sign and nodal solutions for resonant double phase problems

被引：1

作者：

Papageorgiou, Nikolaos S. ^{[1
,2
]}

Radulescu, Vicentiu D. ^{[2
,3
,4
,5
,6
]}

Wang, Yitian ^{[2
,7
]}

机构：

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

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

[3] AGH Univ Krakow, Fac Appl Math, Al Mickiewicza 30, PL-30059 Krakow, Poland

[4] Brno Univ Technol, Fac Elect Engn & Commun, Tech 3058-10, Brno 61600, Czech Republic

[5] Romanian Acad, Sim Stoilow Inst Math, Bucharest 010702, Romania

[6] Zhejiang Normal Univ, Sch Math, Jinhua 321004, Zhejiang, Peoples R China

[7] Harbin Engn Univ, Coll Math Sci, Harbin 150001, Peoples R China

来源：

ANNALES FENNICI MATHEMATICI | 2023年 / 48卷 / 02期

关键词：

Double phase operator; unbalanced growth; generalized Orlicz spaces; resonant equation; multiple solutions with sign information; ELLIPTIC-EQUATIONS; EXISTENCE; REGULARITY; CALCULUS;

D O I：

10.54330/afm.141250

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider a double phase Dirichlet problem with a reaction which asymptotically as x -> +/- (infinity )can be resonant with respect to the principle eigenvalue lambda(1) > 0 of the Dirichlet weighted p-Laplacian. Using variational tools, together with truncation and comparison techniques and critical groups, we show that the problem has at least three bounded solutions which are ordered and we provide sign information for all of them (positive, negative and nodal).

引用

页码：757 / 777

页数：21

共 25 条

[1]

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

[2] A Multiplicity Theorem for Superlinear Double Phase Problems [J].

Deregowska, Beata ;

Gasinski, Leszek ;

Papageorgiou, Nikolaos S. .

SYMMETRY-BASEL, 2021, 13 (09)

[3]

DIAZ JI, 1987, CR ACAD SCI I-MATH, V305, P521

[4] Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian [J].

Filippakis, Michael E. ;

Papageorgiou, Nikolaos S. .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (07) :1883-1922

[5]

Gasinski L., 2016, Problem Books in Mathematics

[6]

Gasinski L., 2006, NONLINEAR ANAL-THEOR

[7] Constant sign and nodal solutions for superlinear double phase problems [J].

Gasinski, Leszek ;

Papageorgiou, Nikolaos S. .

ADVANCES IN CALCULUS OF VARIATIONS, 2021, 14 (04) :613-626

[8] Constant sign solutions for double phase problems with superlinear nonlinearity [J].

Gasinski, Leszek ;

Winkert, Patrick .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2020, 195

[9] QUASILINEAR ELLIPTIC-EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS [J].

GUEDDA, M ;

VERON, L .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1989, 13 (08) :879-902

[10] Orlicz Spaces and Generalized Orlicz Spaces [J].

Harjulehto, Petteri ;

Hasto, Peter .

ORLICZ SPACES AND GENERALIZED ORLICZ SPACES, 2019, 2236 :V-+

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