2017/08/22 by Antonio Iannizzotto, Iannizzotto, Antonio, Nikolaos S. Papageorgiou +2
Computer Science · Mathematics · #35P05 #35R11 #49F15 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Spectral Theory in Mathematical Physics #math.AP #msc:35P05 #msc:35R11 #msc:49F15
paper · pdf · doi:10.48550/arxiv.1708.06668
arxiv created 2017/08/22 · openalex publication_date 2017/08/22 · arxiv updated 2017/08/23 · openalex created_date 2022/09/07 · openalex updated_date 2026/07/28
We study a Dirichlet-type boundary value problem for a pseudo-differential equation driven by the fractional Laplacian, with a non-linear reaction term which is resonant at infinity between two non-principal eigenvalues: for such equation we prove existence of a non-trivial solution. Under further assumptions on the behavior of the reaction at zero, we detect at least three non-trivial solutions (one positive, one negative, and one of undetermined sign). All results are based on the properties of weighted fractional eigenvalues, and on Morse theory.