Abstract. In this work we study the following singular problem involving the fractional Laplace operator:where Ω ⊂ R N , 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 T r,γ such that for all λ ∈ (0,T r,γ ) , problem (P λ ) has at least two solutions.Mathematics subject classification (2010): 34B15, 37C25, 35R20.
This article investigates the source identification in the fractional diffusion equations, by performing a single measurement of the Cauchy data on the accessible boundary. The main results of this work consist in giving an identifiability result and establishing a local Lipschitz stability result. To solve the inverse problem of identifying fractional sources from such observations, a non-iterative algebraical method based on the Reciprocity Gap functional is proposed.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.