Extremal solutions of \(p\)-Laplacian problems in \(D^{1, p}(\mathbb{R}^N)\) via Wolff potential estimates (Q2358272)

The author shows the existence of extremal constant-sign solutions for an elliptic problem of \(p\)-Laplacian logistic type on \(\mathbb R^N\). The assumptions are weaker with respect to preceding works involving the ordinary Laplacian. Furthermore, the problem perturbed with a harvesting term is studied and a strong maximum principle is established. Estimates via Wolff potential and a sub-supersolution principle are given too.