A Multiplicity Theorem for Superlinear Double Phase Problems

被引：6

作者：

Deregowska, Beata ^{[1
]}

Gasinski, Leszek ^{[2
]}

Papageorgiou, Nikolaos S. ^{[3
]}

机构：

[1] Pedag Univ Cracow, Dept Math, Podchorazych 2, PL-30084 Krakow, Poland

[2] State Higher Vocat Sch Tarnow, Inst Math & Nat Sci, Mickiewicza 8, PL-33100 Tarnow, Poland

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

来源：

SYMMETRY-BASEL | 2021年 / 13卷 / 09期

关键词：

double phase operator; Nehari manifold; superlinear reaction; constant sign and nodal solutions; Musielak-Orlicz spaces; REGULARITY; EXISTENCE; CALCULUS;

D O I：

10.3390/sym13091556

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

We consider a nonlinear Dirichlet problem driven by the double phase differential operator and with a superlinear reaction which need not satisfy the Ambrosetti-Rabinowitz condition. Using the Nehari manifold, we show that the problem has at least three nontrivial bounded solutions: nodal, positive and by the symmetry of the behaviour at +infinity and -infinity also negative.

引用

页数：23

共 50 条

[31] Existence and multiplicity of solutions for double-phase Robin problems [J].

Papageorgiou, Nikolaos S. ;

Radulescu, Vicentiu D. ;

Repovs, Dusan D. .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2020, 52 (03) :546-560

[32] Existence and Multiplicity Results for Kirchhoff-Type Problems on a Double-Phase Setting [J].

Fiscella, Alessio ;

Pinamonti, Andrea .

MEDITERRANEAN JOURNAL OF MATHEMATICS, 2023, 20 (01)

[33] Identification of discontinuous parameters in double phase obstacle problems [J].

Zeng, Shengda ;

Bai, Yunru ;

Winkert, Patrick ;

Yao, Jen-Chih .

ADVANCES IN NONLINEAR ANALYSIS, 2023, 12 (01) :1-22

[34] Anisotropic double-phase problems with indefinite potential: multiplicity of solutions [J].

Nikolaos S. Papageorgiou ;

Dongdong Qin ;

Vicenţiu D. Rădulescu .

Analysis and Mathematical Physics, 2020, 10

[35] A multiplicity theorem for Neumann problems with asymmetric nonlinearity [J].

Papageorgiou, Nikolaos S. ;

Smyrlis, George .

ANNALI DI MATEMATICA PURA ED APPLICATA, 2010, 189 (02) :253-272

[36] Constant sign and nodal solutions for resonant double phase problems [J].

Papageorgiou, Nikolaos S. ;

Radulescu, Vicentiu D. ;

Wang, Yitian .

ANNALES FENNICI MATHEMATICI, 2023, 48 (02) :757-777

[37] Existence and multiplicity results for double phase problem with nonlinear boundary condition [J].

Cui, Na ;

Sun, Hong-Rui .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2021, 60

[38] Singular double phase problems with convection [J].

Papageorgiou, Nikolaos S. ;

Peng, Zijia .

NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2025, 81

[39] On a class of critical double phase problems [J].

Farkas, Csaba ;

Fiscella, Alessio ;

Winkert, Patrick .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2022, 515 (02)

[40] On a double phase problem with sublinear and superlinear nonlinearities [J].

Wang, Ke-Qi ;

Zhou, Qing-Mei .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2021, 66 (6-7) :1182-1193

← 1 2 3 4 5 →