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 Rn with 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 / Fiscella A.; Pinamonti A.; Vecchi E.. - In: JOURNAL OF DIFFERENTIAL EQUATIONS. - ISSN 0022-0396. - ELETTRONICO. - 263:8(2017), pp. 4617-4633. [10.1016/j.jde.2017.05.028]
Multiplicity results for magnetic fractional problems
Vecchi E.
2017
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 Rn with 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
