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• W3120448085 abstract "Goal of this paper is to study positive semiclassical solutions of the nonlinear Schrodinger equation $$ varepsilon^{2s}(- Delta)^s u+ V(x) u= f(u), quad x in mathbb{R}^N,$$ where $s in (0,1)$, $N geq 2$, $V in C(mathbb{R}^N,mathbb{R})$ is a positive potential and $f$ is assumed critical and satisfying general Berestycki-Lions type conditions. We obtain existence and multiplicity for $varepsilon>0$ small, where the number of solutions is related to the cup-length of a set of local minima of $V$. Furthermore, these solutions are proved to concentrate in the potential well, exhibiting a polynomial decay. We highlight that these results are new also in the limiting local setting $s=1$ and $Ngeq 3$, with an exponential decay of the solutions." @default.
• W3120448085 created "2021-01-18" @default.
• W3120448085 creator A5009162407 @default.
• W3120448085 date "2021-01-02" @default.
• W3120448085 modified "2023-09-27" @default.
• W3120448085 title "Multiplicity and concentration results for local and fractional NLS equations with critical growth" @default.
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• W3120448085 hasPublicationYear "2021" @default.
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