Odd periodic solutions of fully second-order ordinary differential equations with superlinear nonlinearities
type: Item
instance of: scholarly article
title: Odd periodic solutions of fully second-order ordinary differential equations with superlinear nonlinearities
zbMATH Open document ID: 1378.34065
DOI: 10.1155/2017/4247365
author: Yongxiang Li
author: Lanjun Guo
published in: Journal of Function Spaces
publication date: 2017-11-01T00:00:00Z
review text: Summary: This paper is concerned with the existence of periodic solutions for the fully second-order ordinary differential equation \[ u^{\prime\prime}(t) = f(t, u(t), u^{\prime}(t)), \quad t \in \mathbb{R}, \] where the nonlinearity \(f : \mathbb{R}^3 \rightarrow \mathbb{R}\) is continuous and \(f(t, x, y)\) is \(2 \pi\)-periodic in \(t\). Under certain inequality conditions such that \(f(t, x, y)\) may have superlinear growth on \((x, y)\), the existence of odd \(2 \pi\)-periodic solutions is obtained via the Leray-Schauder fixed point theorem.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 37C60
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 6802000
zbMATH Keywords: superlinear growth
zbMATH Keywords: Leray-Schauder fixed point theorem
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4247365
OpenAlex ID: W2750419498
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description: scientific article; zbMATH DE number 6802000