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

2022/04/04 by Missaoui, Hlel, Ounaies, Hichem
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2204.01648

Abstract

We consider a non-local Shrödinger problem driven by the fractional Orlicz g-Laplace operator as follows (-\triangle_g)^αu+g(u)=K(x)f(x,u), in ℝ^d, where d≥ 3, (-\triangle_g)^α is the fractional Orlicz g-Laplace operator, f:ℝ^d×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 \eqrefPP has a ground state of fixed sign and a nodal (or sign-changing) solutions.

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