Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian

被引：14

作者：

Frassu, Silvia ^{[1
]}

Iannizzotto, Antonio ^{[1
]}

机构：

[1] Univ Cagliari, Dept Math & Comp Sci, Via Osped 72, I-09124 Cagliari, Italy

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2021年 / 501卷 / 01期

关键词：

Fractional p-Laplacian; Extremal constant sign solutions; Nodal solutions; Critical point theory; NONLINEAR EQUATIONS; DIRICHLET PROBLEM; REGULARITY;

D O I：

10.1016/j.jmaa.2020.124205

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study a pseudo-differential equation driven by the degenerate fractional p Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques. (c) 2020 Elsevier Inc. All rights reserved.

引用

页数：22

共 50 条

[1] Multiple constant sign and nodal solutions for nonlinear elliptic equations with the p-Laplacian
Filippakis, Michael E.
Papageorgiou, Nikolaos S.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2008, 245 (07) : 1883 - 1922
[2] Nodal and multiple constant sign solutions for resonant p-Laplacian equations with a nonsmooth potential
Gasinski, Leszek
Papageorgiou, Nikolaos S.
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 71 (11) : 5747 - 5772
[3] Nodal Solutions of the p-Laplacian with Sign-Changing Weight
Ma, Ruyun
Liu, Xilan
Xu, Jia
ABSTRACT AND APPLIED ANALYSIS, 2013,
[4] Constant Sign and Nodal Solutions for Problems with the p-Laplacian and a Nonsmooth Potential Using Variational Techniques
Agarwal, Ravi P.
Filippakis, Michael E.
O'Regan, Donal
Papageorgiou, Nikolaos S.
BOUNDARY VALUE PROBLEMS, 2009, : 1 - 32
[5] CONSTANT-SIGN AND NODAL SOLUTIONS TO A DIRICHLET PROBLEM WITH p-LAPLACIAN AND NONLINEARITY DEPENDING ON A PARAMETER
Marano, Salvatore A.
Papageorgiou, Nikolaos S.
PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 2014, 57 (02) : 521 - 532
[6] Sign-Changing Solutions of Fractional p-Laplacian Problems
Chang, Xiaojun
Nie, Zhaohu
Wang, Zhi-Qiang
ADVANCED NONLINEAR STUDIES, 2019, 19 (01) : 29 - 53
[7] Nodal solutions of a p-Laplacian equation
Bartsch, T
Liu, ZL
Weth, T
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 2005, 91 : 129 - 152
[8] Extremal solutions for nonlinear fractional boundary value problems with p-Laplacian
Ding, Youzheng
Wei, Zhongli
Xu, Jiafa
O'Regan, Donal
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 288 : 151 - 158
[9] MULTIPLE SOLUTIONS FOR A FRACTIONAL p-LAPLACIAN EQUATION WITH SIGN -CHANGING POTENTIAL
Ambrosio, Vincenzo
ELECTRONIC JOURNAL OF DIFFERENTIAL EQUATIONS, 2016,
[10] CONSTANT-SIGN AND NODAL SOLUTIONS FOR A NEUMANN PROBLEM WITH p-LAPLACIAN AND EQUI-DIFFUSIVE REACTION TERM
Marano, Salvatore A.
Papageorgiou, Nicolaos S.
TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 2011, 38 (02) : 233 - 248

← 1 2 3 4 5 →