Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition

We consider a non-local Shrodinger problem driven by the fractional Orlicz g-Laplace operator as follows (-Delta(g))(alpha)u + g(u) = K(x)f(x, u), in R-d, (P) where d >= 3, (-Delta(g))(alpha) is the fractional Orlicz g-Laplace operator, f : R-d x R -> R is a measurable function and K is a positive continuous function. Employing the Nehari manifold method and without assuming the well-known Ambrosetti-Rabinowitz and differentiability conditions on the non-linear term f, we prove that the problem (P) has a ground state of fixed sign and a nodal (or sign-changing) solutions. (c) 2022 Elsevier Inc. All rights reserved.