A quasilinear Neumann problem involving the image-Laplacian Original Research Article

We study the following Neumann problem: View the MathML source{−Δp(x)u+α(x)|u|p(x)−2u=α(x)f(u)+λg(x,u)in Ω∂u∂ν=0on ∂Ω Turn MathJax on and we prove that, under suitable assumptions on the functions αα, ff, pp and gg, the Ricceri two-local-minima theorem, together with the Palais–Smale property, ensures the existence of at least three solutions of it. This work could be considered a possible extension of some results by Cammaroto, Chinnì and Di Bella who handled the case where p(x)p(x) is constant.