Multiple solutions for Robin ( p , q )-equations plus an indefinite potential and a reaction concave near the origin

AbstractWe consider a Robin problem driven by the (p, q)-Laplacian plus an indefinite potential term. The reaction is either resonant with respect to the principal eigenvalue or$$(p-1)$$(p-1)-superlinear but without satisfying the Ambrosetti-Rabinowitz condition. For both cases we show that the problem has at least five nontrivial smooth solutions ordered and with sign information. When$$q=2$$q=2(a (p, 2)-equation), we show that we can slightly improve the conclusions of the two multiplicity theorems