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

In this paper, we study the Schrodinger 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.In this paper, we study the Schrodinger 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.