Existence of a nonnegative bound state for a higher-order logarithmic Schrödinger equation

Xin Ou, Xingyong Zhang, Yanhong Li

In this paper, we study the existence of nonnegative bound states for the higher-order logarithmic Schrödinger equation $$ -αΔu+V(x)u-βu\ln|u| = γu(\ln|u|)^m, \qquad u\in H^1(\math…