The Nehari manifold for a singular elliptic equation involving the fractional Laplace operator

By A. Ghanmi, Kamel Saoudi. 2016

74 citations recorded by the source corpus.

In this work we study the following singular problem involving the fractional Laplace operator: (Pλ ) { L u = a(x) uγ +λ f (x,u) in Ω; u = 0, in RN \Ω, where Ω ⊂ RN , N 2 be a bounded smooth domain, a ∈C(Ω), λ is a positive parameter and 0 < γ < 1, 2 < r < 2∗s where 2∗s = N2 N−2s . Under appropriate assumptions on the function K and the function f and we employ the method of Nehari manifold in order to show the existence of Tr,γ such that for all λ ∈ (0,Tr,γ ) , problem (Pλ ) has at least two solutions. Mathematics subject classification (2010): 34B15, 37C25, 35R20.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/91afdf2406d4c52001c61cc97cc5a14083b671a6

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In Applied Mathematics

1. A. Ghanmi
2. Kamel Saoudi

In Mathematical Physics

1. A. Ghanmi
2. Kamel Saoudi

Citations in the corpus

• A multiplicity results for a singular equation involving the p(x)-Laplace operator (2017, methodology): “Ghanmi–Saoudi [14] investigated the multiplicity of solution for a singular problem involving the fractional Laplace operator using the method of Nehari manifold.”