2022/11/11 by Guglielmo Feltrin, Feltrin, Guglielmo, Juan Carlos Sampedro +3
Mathematics · #34B15 #34B18 #34C25 #47H11 #Advanced Differential Equations and Dynamical Systems #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2211.06070
openalex publication_date 2022/11/11 · openalex created_date 2022/11/21 · openalex updated_date 2026/07/28
We deal with a planar differential system of the form \begincases u' = h(t,v),
v' = - λa(t) g(u), \endcases where h is T-periodic in the first variable and strictly increasing in the second variable, λ>0, a is a sign-changing T-periodic weight function and g is superlinear. Based on the coincidence degree theory, in dependence of λ, we prove the existence of T-periodic solutions (u,v) such that u(t)>0 for all t∈ℝ. Our results generalize and unify previous contributions about Butler's problem on positive periodic solutions for second-order differential equations (involving linear or ϕ-Laplacian-type differential operators).