On a generalized pseudorelativistic Schr\"odinger 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.