Asymptotically linear Dirichlet problem for the \(p\)-Laplacian (Q5932182)

The authors study the existence of positive solutions for the Dirichlet problem \(-\Delta_p u(x)\equiv -\text{div}(\nabla u|^{p-2}\nabla u)= f(x,u)\), \(x\in\Omega\), \(u\in W^{1,p}_0(\Omega)\), where \(p> 1\), \(\Omega\) is a bounded domain in \(\mathbb{R}^N\) \((N\geq 1)\) with smooth boundary \(\partial\Omega\), and \(f\) is asymptotically linear with respect to \(u\) at infinity.