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Research Article | Open Access

Solutions for a class of problems driven by an anisotropic ( p , q )-Laplacian type operator

Center of Sciences and Technology, Federal University of Cariri, Juazeiro do Norte/CE, CEP: 63048-080, Brazil
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Abstract

In this manuscript, existence and multiplicity results are obtained for a problem involving an anisotropic ( p , q )-Laplacian-type operator by means of sub-supersolutions and variational techniques. This problem arises in various applications such as in the study of the enhancement of images, the spread of epidemic disease and in the dynamic of fluids. Under a general condition, the existence of a solution is proved, and the multiplicity of solutions is obtained by considering an additional natural hypothesis.

Keywords

(p, q)-Laplacian type operatoranisotropic operator, sub-supersolutionsexistencemultiplicity
CLC number: 35A15, 35J60

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Communications in Analysis and Mechanics
Volume 15 Issue 3,
September 2023
Pages 533-550
DOI: 10.3934/cam.2023026

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Cite this article:
Tavares L. Solutions for a class of problems driven by an anisotropic ( p , q )-Laplacian type operator. Communications in Analysis and Mechanics, 2023, 15(3): 533-550. https://doi.org/10.3934/cam.2023026

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Received: 06 July 2023
Revised: 03 September 2023
Accepted: 03 September 2023
Published: 15 September 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)