Infinitely many nodal solutions for generalized logistic equations without odd symmetry on reaction

Abstract

We consider nonlinear parametric logistic type equations driven by a nonlinear nonhomogeneous differential operator. The reaction term is a Carathéodory function which is not assumed to be odd. The subdiffusive, equidiffusive and superdiffusive cases are all treated. We prove the existence of infinitely many nodal solutions. We also prove a bifurcation-type result describing the dependence of the set of constant sign solutions on the parameter in the superdiffusive case. Our approach uses variational methods together with upper-lower solutions and truncation techniques, and flow invariance arguments.