The Nehari manifold for a class of Schrödinger equation involving fractional p-Laplacian and sign-changing logarithmic nonlinearity

Abstract

In this paper, we study the Schrödinger equation involving fractional p-Laplacian on the whole space of the form (−Δ)psu+V(x)|u|p−2u=λK(x)|u|p−2u+μQ(x)|u|p−2u⁡log|u|, with the sign-changing weight function Q and the possibly vanishing potential V. By using the relationship between fibering maps and the Nehari manifold, we obtain the existence of at least two nontrivial solutions.