The Nehari manifold for fractional -Laplacian equation with logarithmic nonlinearity on whole space

Abstract

We study a fractional p-Laplacian equation in the whole space with the sign-changing logarithmic nonlinearity. By using fibrering maps and Nehari manifold we obtain the existence of at least two nontrivial solutions. Our result extends a recent result by Tian (2017). The main difficulty is the lack of logarithmic Sobolev inequality concerning to fractional p-Laplacian.