Nonlinear eigenvalue problems for the (p, q)-Laplacian

被引：18

作者：

Papageorgiou, Nikolaos S. ^{[1
]}

Qin, Dongdong ^{[2
]}

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

机构：

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

[2] Cent South Univ, Sch Math & Stat, Changsha 410083, Hunan, Peoples R China

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

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

来源：

BULLETIN DES SCIENCES MATHEMATIQUES | 2021年 / 172卷

基金：

中国国家自然科学基金;

关键词：

(p; q)-Laplacian; Constant sign and nodal solutions; Critical groups; Unique continuation; Nonlinear regularity; INDEFINITE; EXISTENCE; INFINITY; PLUS;

D O I：

10.1016/j.bulsci.2021.103039

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider a parametric (p, q)-equations with sign-changing reaction and Robin boundary condition. We show that for all values of the parameter.bigger than a certain value which we determine precisely, the problem has at least three nontrivial solutions all with sign information and ordered. For the particular case of (p, 2)-equations we produce a second nodal solution, for a total of four nontrivial solutions. Under symmetry conditions, we show the existence of infinitely many nodal solutions. The same results are also valid for the Dirichlet problem. (c) 2021 The Author(s). Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

引用

页数：29

共 50 条

[21] ON THE NONLINEAR EIGENVALUE PROBLEMS INVOLVING THE FRACTIONAL p-LAPLACIAN OPERATOR WITH SINGULAR WEIGHT
Harcha, H.
Chakrone, O.
Tsouli, N.
JOURNAL OF NONLINEAR FUNCTIONAL ANALYSIS, 2022, 2022
[22] A singular eigenvalue problem for the Dirichlet (p, q)-Laplacian
Bai, Yunru
Papageorgiou, Nikolaos S.
Zeng, Shengda
MATHEMATISCHE ZEITSCHRIFT, 2022, 300 (01) : 325 - 345
[23] ON THE NONLINEAR EIGENVALUE PROBLEMS INVOLVING THE FRACTIONAL p-LAPLACIAN OPERATOR WITH SINGULAR WEIGHT
Harcha H.
Chakrone O.
Tsouli N.
Journal of Nonlinear Functional Analysis, 2022, 2022
[24] Asymptotic behaviour of nonlinear eigenvalue problems involving p-Laplacian-type operators
Champion, Thierry
De Pascale, Luigi
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 2007, 137 : 1179 - 1195
[25] EIGENVALUE PROBLEMS FOR THE P-LAPLACIAN WITH INDEFINITE WEIGHTS
Cuesta, Mabel
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2001,
[26] Remarks on eigenvalue problems involving the p(x)-Laplacian
Fan, Xianling
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2009, 352 (01) : 85 - 98
[27] EIGENVALUE PROBLEMS FOR A CLASS OF NONLINEAR HADAMARD FRACTIONAL DIFFERENTIAL EQUATIONS WITH p-LAPLACIAN OPERATOR
Yang, Wengui
MATHEMATICA SLOVACA, 2020, 70 (01) : 107 - 124
[28] Full description of the eigenvalue set of the Steklov (p, q)-Laplacian
Barbu, Luminita
Morosanu, Gheorghe
JOURNAL OF DIFFERENTIAL EQUATIONS, 2021, 290 : 1 - 16
[29] SIMPLICITY AND STABILITY OF THE FIRST EIGENVALUE OF A (p; q) LAPLACIAN SYSTEM
Afrouzi, Ghasem A.
Mirzapour, Maryam
Zhang, Qihu
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2012,
[30] THE FIRST EIGENVALUE OF SOME (p, q)-LAPLACIAN AND GEOMETRIC ESTIMATES
Azami, Shahroud
COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 33 (01): : 317 - 323

← 1 2 3 4 5 →