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

摘要

In this paper, we study the existence of least-energy nodal (sign-changing) weak solutions for a class of fractional Orlicz equations given by (-Delta(g))(alpha)u + g(u) = K(x)f (u), in R-N, where N >= 3, (-Delta(g))(alpha) is the fractional Orlicz g-Laplace operator, while f is an element of 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 OrliczSobolev 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.