Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian-Reference-Cited by-同舟云学术

Existence and Multiplicity of Weak Solutions for a Neumann Elliptic Problem with -Laplacian

Published:2020-01-01 Issue:1 Volume:7 Page:53-64
ISSN:2353-0626
Container-title:Nonautonomous Dynamical Systems
language:en
Short-container-title:

Author:

Bohner Martin¹,Caristi Giuseppe²,Gharehgazlouei Fariba³,Heidarkhani Shapour³

Affiliation:

1. Missouri S&T, Department of Mathematics and Statistics , Rolla , MO 65409, USA

2. University of Messina , Department of Economics , Messina , Italy

3. Razi University , Department of Mathematics, Faculty of Sciences , 67149 Kermanshah, Iran

Abstract

Abstract We are interested in the existence of multiple weak solutions for the Neumann elliptic problem involving the anisotropic -Laplacian operator, on a bounded domain with smooth boundary. We work on the anisotropic variable exponent Sobolev space, and by using a consequence of the local minimum theorem due to Bonanno, we establish existence of at least one weak solution under algebraic conditions on the nonlinear term. Also, we discuss existence of at least two weak solutions for the problem, under algebraic conditions including the classical Ambrosetti–Rabinowitz condition on the nonlinear term. Furthermore, by employing a three critical point theorem due to Bonanno and Marano, we guarantee the existence of at least three weak solutions for the problem in a special case.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Numerical Analysis,Statistics and Probability,Analysis

Link

https://www.degruyter.com/document/doi/10.1515/msds-2020-0108/pdf

Reference31 articles.

1. [1] Ghasem A. Afrouzi, Martin Bohner, Giuseppe Caristi, Shapour Heidarkhani, and Shahin Moradi. An existence result for impulsive multi-point boundary value systems using a local minimization principle. J. Optim. Theory Appl., 177(1):1–20, 2018.

2. [2] Ahmed Ahmed, Mohamed Saad Bouh Elemine Vall, Abdelmoujib Benkirane, and Abdelfattah Touzani. Existence of infinitely many solutions to the Neumann problem for quasilinear elliptic systems involving the p(·) and q(·)-Laplacian. Nonlinear Stud., 24(3):687–698, 2017.

3. [3] Ahmed Ahmed, Hassane Hjiaj, and Abdelfattah Touzani. Existence of infinitely many weak solutions for a Neumann elliptic equations involving the -Laplacian operator. Rend. Circ. Mat. Palermo (2), 64(3):459–473, 2015.

4. [4] Ahmed Ahmed, Abdelfettah Touzani, and Youssef Akdim. Infinitely many solutions for an elliptic Neumann problem in weighted variable exponent Sobolev spaces. J. Nonlinear Evol. Equ. Appl., Paper No. 2, 15–34, 2019.

5. [5] Stanislav N. Antontsev and José F. Rodrigues. On stationary thermo-rheological viscous flows. Ann. Univ. Ferrara Sez. VII Sci. Mat., 52(1):19–36, 2006.

Cited by 5 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Weak Solutions for a System Involving Anisotropic $$\left( \overrightarrow{p}(\cdot ), \overrightarrow{q}(\cdot )\right) $$-Laplacian Operators;Iranian Journal of Science;2024-05-04

2. Existence and multiplicity of solutions to a fractional p-Laplacian elliptic Dirichlet problem;Electronic Journal of Differential Equations;2023-07-03

3. Solutions of an anisotropic elliptic problem involving nonlinear terms;Quaestiones Mathematicae;2023-04-12

4. Weak solutions for elliptic problems in weighted anisotropic Sobolev space;Filomat;2023

5. PERTURBED NONLINEAR ELLIPTIC NEUMANN PROBLEMS INVOLVING ANISOTROPIC SOBOLEV SPACES WITH VARIABLE EXPONENTS;MATEMATICHE;2022