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Double-phase problems and a discontinuity property of the spectrum

Published 5 Jun 2019 in math.AP | (1906.01924v2)

Abstract: We consider a nonlinear eigenvalue problem driven by the sum of $p$ and $q$-Laplacian. We show that the problem has a continuous spectrum. Our result reveals a discontinuity property for the spectrum of a parametric ($p,q$)-differential operator as the parameter $\beta\rightarrow 1-$.

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