The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian (−Δ)A s, that is (−Δ)A su=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.
Fiscella, A., Pinamonti, A., Vecchi, E. (2017). Multiplicity results for magnetic fractional problems. JOURNAL OF DIFFERENTIAL EQUATIONS, 263(8), 4617-4633 [10.1016/j.jde.2017.05.028].
Multiplicity results for magnetic fractional problems
Fiscella A;
2017
Abstract
The paper deals with the existence of multiple solutions for a boundary value problem driven by the magnetic fractional Laplacian (−Δ)A s, that is (−Δ)A su=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.
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