The coexistence of quasi-periodic and blow-up solutions in a superlinear Duffing equation

2017/05/24 by Sun, Yanmei, Li, Xiong
#Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1705.08763

Abstract

In this paper we will construct a continuous positive periodic function p(t) such that the corresponding superlinear Duffing equation x"+a(x) x²ⁿ⁺¹+p(t) x^2m+1=0, n+2≤ 2m+1lt;2n+1 possesses a solution which escapes to infinity in some finite time, and also has infinitely many subharmonic and quasi-periodic solutions, where the coefficient a(x) is an arbitrary positive smooth periodic function defined in the whole real axis.

Related

• Periodic solutions of semilinear Duffing equations with impulsive effects
• Existence, uniqueness, and stability of periodic solutions of an equation of Duffing type
• Multiplicity of positive periodic solutions in the superlinear indefinite case via coincidence degree
• Rate of Decay of Stable Periodic Solutions of Duffing Equations
• Positive solutions for super-sublinear indefinite problems: high multiplicity results via coincidence degree