Positive solutions for resonant \((p, q)\)-equations with concave terms (Q1660079)

This paper deals with the qualitative analysis of positive solutions of a class of \((p,q)\)-equations with nonlinear Robin boundary condition. The reaction exhibits the competing effects of two nonlinearities, namely a parametric concave term and a resonant Carathéodory perturbation. The main result of this paper establishes that the equation has at least two positive smooth solutions for all small positive values (low perturbations) of a certain parameter. The proof is based on refined variational methods based on the critical point theory together with suitable truncation and comparison techniques. The reviewer expects that the methods introduced in this paper will be extended to other classes of nonlinear elliptic PDEs.