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

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 ) α u + g ( u ) = K ( x ) f ( u ) , in R N , where N ⩾ 3 , ( − △ g ) α is the fractional Orlicz g-Laplace operator, while f ∈ C 1 ( 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.