Non-autonomous Eigenvalue Problems with Variable (p 1,p 2)-Growth-Reference-Cited by-同舟云学术

Non-autonomous Eigenvalue Problems with Variable (p 1,p 2)-Growth

Published:2017-02-17 Issue:4 Volume:17 Page:781-792
ISSN:2169-0375
Container-title:Advanced Nonlinear Studies
language:en
Short-container-title:

Author:

Baraket Sami¹,Chebbi Souhail²,Chorfi Nejmeddine²,Rădulescu Vicenţiu D.³

Affiliation:

1. Département de Mathématiques , Faculté des Sciences de Tunis , Campus Universitaire, 2092 Tunis , Tunisia

2. Department of Mathematics, College of Sciences , King Saud University , Box 2455 , Riyadh 11451 , Saudi Arabia

3. Institute of Mathematics “Simion Stoilow” of the Romanian Academy , P.O. Box 1-764, 014700 Bucharest ; and Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585 Craiova , Romania

Abstract

Abstract We are concerned with the study of a class of non-autonomous eigenvalue problems driven by two non-homogeneous differential operators with variable ( p 1 , p 2 )

{(p_{1},p_{2})}

-growth. The main result of this paper establishes the existence of a continuous spectrum consisting in an unbounded interval and the nonexistence of eigenvalues in a neighbourhood of the origin. The abstract results of this paper are described by two Rayleigh-type quotients and the proofs rely on variational arguments.

Funder

National Plan for Science, Technology and Innovation

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics,Statistical and Nonlinear Physics

Link

https://www.degruyter.com/document/doi/10.1515/ans-2016-6020/pdf

Reference20 articles.

1. P. Baroni, M. Colombo and G. Mingione, Non-autonomous functionals, borderline cases and related function classes, St. Petersburg Math. J. 27 (2016), 347–379. 10.1090/spmj/1392

2. M. Cencelj, D. Repovš and Z. Virk, Multiple perturbations of a singular eigenvalue problem, Nonlinear Anal. 119 (2015), 37–45. 10.1016/j.na.2014.07.015

3. F. Colasuonno and P. Pucci, Multiplicity of solutions for p⁢(x){p(x)}-polyharmonic elliptic Kirchhoff equations, Nonlinear Anal. 74 (2011), no. 17, 5962–5974.