Infinitely many sign-changing solutions of a critical fractional equation

Abstract

In this paper we prove the existence of an unbounded sequence of sign changing solutions to a laplacian fractional and critical problem in the Euclidean space by reducing the initial problem to an equivalent problem on the Euclidean unit sphere and exploring its symmetries.

Entire sign-changing solutions to the fractional critical Schr{ö}dinger equation

“…The key component is that we use the equivariant group to partion Ḣs (R N ) into several connected components, then combine the concentration compactness argument to show the compactness property of Palais-Smale sequences in each component and obtain many solutions of (FCSE) in Ḣs (R N ). Both the solutions and the argument here are different from those by Garrido, Musso in [19] and by Abreu, Barbosa and Ramirez in [1].…”

“…Both the result and the argument in this paper are different from those in [1,19]. Abreu, Barbosa and Ramirez obtained infinitely many sign-changing solutions of (1.1) by the Ljusternik-Schnirelman type mini-max method and group invariant technique in [1]. Garrido and Musso constructed the sign-changing solutions of (1.1) by the LyapunovSchmidt reduction argument in [19].…”

Existence and convergence of solutions to fractional pure critical exponent problems

“…In this sense, the method we present here is more flexible and universal. We emphasize that the solutions given by Theorem 1.3 are different from those obtained in [Din86] for s = 1, in [BSW04] for s ∈ N, and in [ABR19] for s ∈ (0, 1).…”