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February 19, 2026Demonstratio Mathematica0 citationsOpen Access

Monotonicity and symmetry of positive solutions to fractional p ( x , ⋅)-Laplacian equation in bounded and unbounded domains

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PWP. WangXinyang Normal UniversityZWZhihao WangXinyang Normal University

Key Points

  • The research aims to analyze the monotonicity and symmetry of positive solutions to a fractional p-Laplacian equation.
  • Consideration of nonlinear elliptic equations involving fractional p-Laplacian
  • Analysis of positive solutions in bounded and unbounded convex domains
  • Mathematical modeling of solutions using specified conditions
  • Demonstrated symmetry and monotonicity of solutions in the defined domains
  • Established criteria for positive solutions in both bounded and unbounded cases
  • Showed that the solutions maintain specific mathematical properties under the fractional p-Laplacian framework

Abstract

Abstract In this paper, we consider the following nonlinear elliptic equations involving the fractional p (x, ⋅) -Laplacian: (− Δ) p (x, ⋅) s u (x) = g (x, u (x), ∇ u (x) ), x ∈ Ω, u (x) > 0, x ∈ Ω, u (x) ≡ 0, x ∈ R N \ Ω, cases (-{) }₏ (ₗ, ) ^su (x) =g (x, u (x), u (x) ), & x, \\ u (x) >0, & x, \\ u (x) 0, & x R^N, cases where Ω is a bounded or an unbounded domain, which is convex in x 1 -direction and the fractional p (x, ⋅) -Laplacian is defined by (− Δ) p (x

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Cite This Study

Wang et al. (2026) studied this question.

synapsesocial.com/papers/6996a7a5ecb39a600b3ed7e1https://doi.org/10.1515/dema-2025-0214
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  5. 5Monotonicity results for the fractional p-Laplacian in unbounded domains2021 · 5 citations