The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian (−Δ)As, that is (−Δ)Asu=λf(|u|)u in Ω,u=0 in Rn∖Ω, where λ is a real parameter, f is a continuous function and Ω is an open bounded subset of Rnwith Lipschitz boundary. We prove that the problem admits at least two nontrivial weak solutions under two different sets of conditions on the nonlinear term f which are dual in a suitable sense.
Multiplicity results for magnetic fractional problems
Vecchi E.
2017-01-01
Abstract
The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian (−Δ)As, that is (−Δ)Asu=λf(|u|)u in Ω,u=0 in Rn∖Ω, where λ is a real parameter, f is a continuous function and Ω is an open bounded subset of Rnwith Lipschitz boundary. We prove that the problem admits at least two nontrivial weak solutions under two different sets of conditions on the nonlinear term f which are dual in a suitable sense.File in questo prodotto:
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