On a generalized pseudorelativistic Schrödinger equation with supercritical growth

Abstract

We prove that the generalized pseudorelativistic equation $${\left(-c^2\Delta +m^2{c}^{\frac{2}{1-s}}\right)}^{s}u-m^{2s}{c}^{\frac{2s}{1-s}}u+\mu u=|u{|}^{p-1}u$$ can be solved for large values of the "light speed" $c$ even when $p$ crosses the critical value for the fractional Sobolev embedding.

References in corpus (1)

• On critical and supercritical pseudo-relativistic nonlinear Schrödinger equations