Polyharmonic Nonlinear Scalar Field Equations
Abstract
In this paper, we present a result on the existence of ground state solutions for the polyharmonic nonlinear equation (-)m u=g(u), assuming that g has a general subcritical growth at infinity, inspired by Berestycki and Lions BerestyckiLions. In comparison with the biharmonic case studied in Med-Siem, the presence of a higher-order operator gives rise to several analytical challenges, which are overcome in the present work. Furthermore, we establish a new polyharmonic logarithmic Sobolev inequality.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.