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

2019/11/14 by Silvia Frassu, Frassu, Silvia, Antonio Iannizzotto +1 · 2 citations
Mathematics · Computer Science · #Nonlinear Partial Differential Equations #Advanced Mathematical Modeling in Engineering #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1911.06038

Abstract

We study a pseudo-differential equation driven by the degenerate fractional\np-Laplacian, under Dirichlet type conditions in a smooth domain. First we show\nthat the solution set within the order interval given by a sub-supersolution\npair is nonempty, directed, and compact, hence endowed with extremal elements.\nThen, we prove existence of a smallest positive, a biggest negative and a nodal\nsolution, combining variational methods with truncation techniques.\n

Cited by

• On boundary regularity for the fractional p-Laplacian with unbounded reactions
• Differential inclusion systems with fractional competing operator and multivalued fractional convection term

Related

• Positive solutions for the fractional p-Laplacian via mixed topological and variational methods
• The extremal solution for the fractional Laplacian
• Large solutions for fractional Laplacian operators
• Existence of sign-changing solution for a problem involving the fractional Laplacian with critical growth nonlinearities
• The fractional p-Laplacian evolution equation in \ℝ^N in the\n sublinear case