A pair of nontrivial bounded solutions for parametric nonlinear elliptic equations with unbalanced growth

We consider a parametric Dirichlet problem driven by a nonautonomous (𝑝, 𝑞)-differential operator with unbalanced growth. In the reaction we have the competing effects of a parametric (𝑝−1)-superlinear term and of a (𝑝−1)-linear perturbation. Using variational tools, we show that for all small values of the positive parameter, the problem has at least two nontrivial bounded solutions.