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We investigate the existence and the multiplicity of solutions of the problem$$ \begin{cases} -\Delta_p u-\Delta_q u = g(x, u)\quad & \mbox{in } \Omega,\\\displaystyle{u=0} & \mbox{on } \partial\Omega, \end{cases} $$ where $\Omega$is a smooth, bounded domain of $\mathbb R^N$, $1<p<q<\infty$, and thenonlinearity $g$ behaves as $u^{q-1}$ at infinity. We use variational methodsand find multiple solutions as minimax critical points of the associated energyfunctional. Under suitable assumptions on the nonlinearity, we cover also theresonant case.

Multiple solutions for asymptotically $q$-linear $(p,q)$-Laplacian problems