System of Hill’s Equations: Constant-Sign Periodic Solutions

Ravi P. Agarwal, Donal O’Regan and Patricia J. Y. Wong
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Ravi P. Agarwal: Texas A&M University – Kingsville, Department of Mathematics
Donal O’Regan: National University of Ireland, Galway, School of Mathematics, Statistics and Applied Mathematics
Patricia J. Y. Wong: Nanyang Technological University, School of Electrical & Electronic Engineering

Chapter Chapter 14 in Constant-Sign Solutions of Systems of Integral Equations, 2013, pp 413-441 from Springer

Abstract: Abstract In this chapter we shall consider the system of Hill’s equations $$\displaystyle{ u_{i}^{{\prime}{\prime}}(t) + a_{i}(t)u_{i}(t) = F_{i}(t,u_{1}(t),u_{2}(t),\cdots \,,u_{n}(t)),\ \ 1 \leq i \leq n. }$$ Here, a i and F i are T-periodic in the variable t, $$a_{i} \in {L}^{1}[0,T],$$ and the nonlinearities $$F_{i}(t,x_{1},x_{2},\cdots \,,x_{n})$$ can be singular at x j = 0 where $$j \in \{ 1,2,\cdots \,,n\}$$ . Throughout, let $$u = (u_{1},u_{2},\cdots \,,u_{n})$$ .

Keywords: Positive Periodic Solution; Constant Sign Solutions; Schauder Fixed Point Theorem; Ermakov Pinney Equation; Leray-Schauder Alternative (search for similar items in EconPapers)
Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-01255-1_14

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DOI: 10.1007/978-3-319-01255-1_14

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