Supercritical Trudinger-Moser inequalities with logarithmic weights in dimension two

Leuyacc Y.R.S. · AIMS Mathematics (2023) · DOI: 10.3934/math.2023933

Resumen

In this work, we are interested in studying the existence of nontrivial weak solutions to the following class of Schrödinger equations [formula presented] where w(x) = ln(1/|x|)β for some β ∈ [0, 1), the nonlinearity f (x, s) behaves like exp((1 + h(|x|))|s|2/(1−β)) and h is a continuous radial function such that h(r) tends to infinity as r tends to 1. The proof involves variational methods and a new version of Trudinger-Moser inequality.

Instituciones: Universidad Nacional Mayor de San Marcos