Anisotropic \((\vec{p}, \vec{q})\)-Laplacian problems with superlinear nonlinearities (Q6611940)

The authors study a parametric differential problem whose principal operator is the sum of two anisotropic \(\vec{r}\)-Laplacian operators with \(\vec{r} \in \mathbb{R}^N\), here \(N \geq 2\). The problem is posed in a bounded domain of \(\mathbb{R}^N\) with sufficiently smooth boundary and Dirichlet boundary condition. Hence, it is solved in the appropriate anisotropic Sobolev space, more precisely the authors obtain two nontrivial weak solutions, under certain conditions on the nonlinearity and without imposing the Ambrosetti-Rabinowitz condition. In details, the authors study the energy functional associated to the problem, by applying tools of critical point theory.