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Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator

  • Mohamed El Ouaarabi EMAIL logo , Chakir Allalou and Said Melliani
Published/Copyright: August 4, 2023
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 73 Issue 4

ABSTRACT

The Dirichlet boundary value problem for elliptic equations involving the (p(x), q(x))-Laplacian operator with a reaction term depending on the gradient and on two real parameters is considered in this paper. Using the topological degree theory for a class of demicontinuous operators of generalized (S+) and the theory of the variable exponent Sobolev spaces, we prove the existence of at least one weak solution of such problem.

2020 Mathematics Subject Classification: Primary 35J60; Secondary 35J70; 35D30; 47H11
Keywords: Double phase problem; (p(x), q(x))-Laplacian operators; topological degree methods; variable exponent Sobolev spaces

(Communicated by Alberto Lastra)

Acknowledgement

The authors would like to thank the referees and the editor greatly for their careful reading and the valuable comments and suggestions that substantially helped improving the quality of the paper.

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Received: 2022-01-21
Accepted: 2022-11-04
Published Online: 2023-08-04

© 2023 Mathematical Institute Slovak Academy of Sciences

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  3. The Deranged Bell Numbers
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https://doi.org/10.1515/ms-2023-0072
Keywords for this article
Double phase problem; (p(x), q(x))-Laplacian operators; topological degree methods; variable exponent Sobolev spaces

Articles in the same Issue

  1. A Note on Special Subsets of the Rudin-Frolík Order for Regulars
  2. The 2-Class Group of Certain Families of Imaginary Triquadratic Fields
  3. The Deranged Bell Numbers
  4. On Index and Monogenity of Certain Number Fields Defined by Trinomials
  5. The k-Generalized Lucas Numbers Close to a Power of 2
  6. Shifted Power of a Polynomial with Integral Roots
  7. Further Insights into the Mysteries of the Values of Zeta Functions at Integers
  8. Memoryless Properties on Time Scales
  9. A Study of the Higher-Order Schwarzian Derivatives of Hirotaka Tamanoi
  10. Besov and Triebel-Lizorkin Capacity in Metric Spaces
  11. Oscillation of Odd Order Linear Differential Equations with Deviating Arguments with Dominating Delay Part
  12. An Elliptic Type Inclusion Problem on the Heisenberg Lie Group
  13. Existence Result for a Double Phase Problem Involving the (p(x), q(x))-Laplacian Operator
  14. A New Series Space Derived by Absolute Generalized Nörlund Means
  15. Examples of Weinstein Domains in the Complement of Smoothed Total Toric Divisors
  16. The Uniform Effros Property and Local Homogeneity
  17. Limit Theorems for Weighted Sums of Asymptotically Negatively Associated Random Variables Under Some General Conditions
  18. The Unit-Gompertz Quantile Regression Model for the Bounded Responses
  19. An Extended Gamma-Lindley Model and Inference for the Prediction of Covid-19 in Tunisia
  20. Modeling Bivariate Data Using Linear Exponential and Weibull Distributions as Marginals
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