Sharp homogeneous Gagliardo--Nirenberg inequalities with applications to normalized solutions for a generalized MMT-type equation
Amin Esfahani, Mukhtar Karazym
Abstract
In this paper, we prove the existence of optimizers for a class of sharp homogeneous Gagliardo--Nirenberg inequalities, extending the result of Bellazzini, Frank, and Visciglia Bellazzini2014. As an application, we establish the existence of normalized solutions to the associated Euler--Lagrange equations. In particular, the case p=2 includes the stationary equation arising from the Majda--McLaughlin--Tabak (MMT) model Majda1997.
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