2025/06/05 by Jebelean, Petru, Mawhin, Jean, Serban, Calin
#Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics
paper · doi:10.48550/arxiv.2506.04927
We are concerned with the existence of T-periodic solutions to an equation of type (|u'(t))|p(t)-2 u'(t) )'+f(u(t))u'(t)+g(u(t))=h(t) in [0,T] where p:[0,T]→(1,∞) with p(0)=p(T) and h are continuous on [0,T], f,g are also continuous on [0,∞), respectively (0,∞). The mapping g may have an attractive singularity (i.e. g(x) → +∞ as x→ 0+). Our approach relies on a continuation theorem obtained in the recent paper M. García-Huidobro, R. Manásevich, J. Mawhin and S. Tanaka, J. Differential Equations (2024), a priori estimates and method of lower and upper solutions.