A Multiplicity Theorem for Superlinear Double Phase Problems

被引：5

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

[1] Multiple solutions for superlinear double phase Neumann problems [J].

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

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[4] Parametric superlinear double phase problems with singular term and critical growth on the boundary [J].

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[5] Divergent sequence of nontrivial solutions for superlinear double phase problems [J].

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[6] Nehari manifold approach for superlinear double phase problems with variable exponents [J].

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[7] Multiple solutions for superlinear double phase Neumann problems [J].

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[8] A MULTIPLICITY THEOREM FOR PARAMETRIC SUPERLINEAR (p, q)-EQUATIONS [J].

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[9] Concentration and multiplicity of solutions for fractional double phase problems [J].

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