2020/12/03 by Lisbeth Carrero, Alexander Quaas, Carrero, Lisbeth +1
Mathematics · #35B10 (Primary) 35J60 #35B45 (Secondary) #35J75 #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #Differential Equations and Numerical Methods #FOS: Mathematics #Nonlinear Differential Equations Analysis
paper · pdf · doi:10.48550/arxiv.2012.02313
openalex publication_date 2020/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we prove existence results of a one-dimensional periodic solution to equations with the fractional Laplacian of order s∈(1/2,1), singular nonlinearity, and gradient term under various situations, including nonlocal contra-part of classical Lienard vector equations, as well other nonlocal versions of classical results know only in the context of second-order ODE. Our proofs are based on degree theory and Perron's method, so before that we need to establish a variety of priori estimates under different assumptions on the nonlinearities appearing in the equations. Besides, we obtain also multiplicity results in a regime where a priori bounds are lost and bifurcation from infinity occurs.