Using a minimization argument and a quantitative deformation lemma, we establish the existence of least energy sign-changing solutions for the following nonlinear Kirchhoff problem (a+b[u]2)(−Δ)su+V(x)u=K(x)f(u)inR3,where a,b>0 are constants, s∈(0,1), (−Δ)s is the fractional Laplacian, V,K are continuous, positive functions, allowed for vanishing behavior at infinity, and f is a continuous function satisfying suitable growth assumptions. Moreover, when the nonlinearity f is odd, we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals.

Sign-changing solutions for a fractional Kirchhoff equation

Isernia T.
2020

Abstract

Using a minimization argument and a quantitative deformation lemma, we establish the existence of least energy sign-changing solutions for the following nonlinear Kirchhoff problem (a+b[u]2)(−Δ)su+V(x)u=K(x)f(u)inR3,where a,b>0 are constants, s∈(0,1), (−Δ)s is the fractional Laplacian, V,K are continuous, positive functions, allowed for vanishing behavior at infinity, and f is a continuous function satisfying suitable growth assumptions. Moreover, when the nonlinearity f is odd, we obtain the existence of infinitely many nontrivial weak solutions not necessarily nodals.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11566/289873
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