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A fractional $$p(x,\cdot )$$ p ( x , · ) -Laplacian problem involving a singular term

Author

Listed:
  • A. Mokhtari

    (University of M’sila)

  • K. Saoudi

    (University of Imam Abdulrahman Bin Faisal
    Imam Abdulrahman Bin Faisal University)

  • N. T. Chung

    (Quang Binh University)

Abstract

This paper deals with a class of singular problems involving the fractional $$p(x,\cdot )$$ p ( x , · ) -Laplace operator of the form $$\begin{aligned} \left\{ \begin{array}{ll} (-\Delta )^{s}_{p(x,\cdot )}u(x)= \frac{\lambda }{u^{\gamma (x)}}+u^{q(x)-1} &{} \hbox {in }\Omega , \\ u>0, \;\;\text {in}\;\; \Omega &{} \hbox {} \\ u=0 \;\;\text {on}\;\;{\mathbb {R}}^N\setminus \Omega , &{} \hbox {} \end{array} \right. \end{aligned}$$ ( - Δ ) p ( x , · ) s u ( x ) = λ u γ ( x ) + u q ( x ) - 1 in Ω , u > 0 , in Ω u = 0 on R N \ Ω , where $$\Omega $$ Ω is a smooth bounded domain in $${\mathbb {R}}^N$$ R N ( $$N\ge 3$$ N ≥ 3 ), $$0 0$$ λ > 0 small enough. To our best knowledge, this paper is one of the first attempts in the study of singular problems involving fractional $$p(x,\cdot )$$ p ( x , · ) -Laplace operators.

Suggested Citation

  • A. Mokhtari & K. Saoudi & N. T. Chung, 2022. "A fractional $$p(x,\cdot )$$ p ( x , · ) -Laplacian problem involving a singular term," Indian Journal of Pure and Applied Mathematics, Springer, vol. 53(1), pages 100-111, March.
    • Handle: RePEc:spr:indpam:v:53:y:2022:i:1:d:10.1007_s13226-021-00037-4
    DOI: 10.1007/s13226-021-00037-4
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