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articleNo Access
A multiplicity results for a singular quasilinear elliptic equation
- Mounir Hsini,
- Kamel Saoudi, and
- Mouldi Seddik
International Journal of Mathematics10 Jul 2021
Preview Abstract
The purpose of this work is to study the following singular problem:
$(P_{λ}) \{\begin{matrix} - div (a (x, \nabla u)) = u^{- α} + λ u^{q} & in Ω; \\ u > 0, & in Ω; \\ u = 0, & in ℝ^{n} ∖ Ω; \end{matrix}$
where $Ω \subset ℝ^{N}$ , $N \geq 2$ be a bounded smooth domain, $λ$ is a positive parameter, $p \geq 2$ such that $N \geq p$ and $0 < α \leq 1$ , $p - 1 < q \leq p^{*} - 1,$ where $p^{*} = \frac{N p}{N - p} .$ We employ the Nehari manifold approach and the fibering maps in order to show the existence of $T_{q, α}$ such that for all $λ \in (0, T_{q, α})$ , problem $(P_{λ})$ has at least two solutions.

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