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

Leandro Tavares; Leandro Tavares

doi:10.3934/cam.2023026

Communications in Analysis and Mechanics

2023, Volume 15, Issue 3: 533-550. doi: 10.3934/cam.2023026

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

Leandro Tavares ^,

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

Received: 06 July 2023 Revised: 03 September 2023 Accepted: 03 September 2023 Published: 06 September 2023
35A15, 35J60

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.
- $ (p, q) $-Laplacian type operator,
- anisotropic operator, sub-supersolutions,
- existence,
- multiplicity
Citation: Leandro Tavares. Solutions for a class of problems driven by an anisotropic $ (p, q) $-Laplacian type operator[J]. Communications in Analysis and Mechanics, 2023, 15(3): 533-550. doi: 10.3934/cam.2023026

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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.

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