In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation (−∆)mu = g(u), assuming that g has a general subcritical growth at infinity, inspired by Berestycki and Lions [3]. In comparison with the biharmonic case studied in [21], the presence of a higherorder operator gives rise to several analytical challenges, which are overcome in the present work. Furthermore, we establish a new polyharmonic logarithmic Sobolev inequality
Polyharmonic Nonlinear Scalar Field Equations Nonlinear Analysis
Alessandro Cannone
;Silvia Cingolani;
2026-01-01
Abstract
In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation (−∆)mu = g(u), assuming that g has a general subcritical growth at infinity, inspired by Berestycki and Lions [3]. In comparison with the biharmonic case studied in [21], the presence of a higherorder operator gives rise to several analytical challenges, which are overcome in the present work. Furthermore, we establish a new polyharmonic logarithmic Sobolev inequalityFile in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
