Sign-changing solutions for parametric Neumann problems with broken symmetry and arbitrary growth

Abstract

Abstract We consider a parametric Neumann problem driven by a nonhomogeneous differential operator, with a reaction consisting of a critical term plus a Carathéodory perturbation which is only locally restricted near zero and is not assumed to be odd. Combining variational methods, with upper-lower solutions and truncation techniques, and flow invariance arguments, we show that the problem admits infinitely many sign-changing solutions.