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

We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace operator as follows(P)(−△g)αu+g(u)=K(x)f(x,u),inRd, where d≥3,(−△g)α is operator, f:Rd×R→R measurable function and K positive continuous function. Employing Nehari manifold method without assuming well-known Ambrosetti-Rabinowitz differentiability conditions on non-linear term f, we prove that (P) has ground state of fixed sign nodal (or sign-changing) solutions.