Least-energy nodal solutions of nonlinear equations with fractional Orlicz–Sobolev spaces

Article type: Research Article

Authors: Bahrouni, Anouar^{; *} | Missaoui, Hlel | Ounaies, Hichem

Affiliations: Mathematics Department, Faculty of Sciences, University of Monastir, 5019 Monastir, Tunisia

Correspondence: [*] Corresponding author. E-mails: [email protected], [email protected].

Abstract: In this paper, we study the existence of least-energy nodal (sign-changing) weak solutions for a class of fractional Orlicz equations given by (−△g)αu+g(u)=K(x)f(u),inRN, where N⩾3,(−△g)α is the fractional Orlicz g-Laplace operator, while f ∈C1(R) and K is a positive and continuous function. Under a suitable conditions on f and K, we prove a compact embeddings result for weighted fractional Orlicz–Sobolev spaces. Next, by a minimization argument on Nehari manifold and a quantitative deformation lemma, we show the existence of at least one nodal (sign-changing) weak solution.

Keywords: Nodal solutions, Fractional Orlicz–Sobolev spaces, Nehari manifold method, least energy

DOI: 10.3233/ASY-221770

Journal: Asymptotic Analysis, vol. 131, no. 2, pp. 145-183, 2023