Extremal constant sign solutions and nodal solutions for the fractional p-Laplacian

We study a pseudo-differential equation driven by the degenerate fractional p Laplacian, under Dirichlet type conditions in a smooth domain. First we show that the solution set within the order interval given by a sub-supersolution pair is nonempty, directed, and compact, hence endowed with extremal elements. Then, we prove existence of a smallest positive, a biggest negative and a nodal solution, combining variational methods with truncation techniques. (c) 2020 Elsevier Inc. All rights reserved.