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.

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

Silvia Frassu;Antonio Iannizzotto
2021-01-01

Abstract

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.
2021
Fractional p-Laplacian; Extremal constant sign solutions; Nodal solutions; Critical point theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11584/292078
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