Existence of a periodic solution for superlinear second order ODEs

被引：4

作者：

Gidoni, Paolo ^{[1
,2
,3
]}

机构：

[1] Univ Udine, Polytech Dept Engn & Architecture, Udine, Italy

[2] Czech Acad Sci, Inst Informat Theory & Automat, Prague, Czech Republic

[3] Univ Udine, Dipartimento Politecn Ingn & Architettura, Via Sci 206, I-33100 Udine, Italy

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2023年 / 345卷

关键词：

Periodic solutions; Superlinear differential equations; Rotation; BOUNDARY-VALUE-PROBLEMS; MULTIPLE SOLUTIONS; CONTINUATION; EQUATIONS;

D O I：

10.1016/j.jde.2022.11.054

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove a necessary and sufficient condition for the existence of a T-periodic solution for the time -periodic second order differential equation x spacing diaeresis + f (t, x) + p(t, x, x) = 0, where f grows superlinearly in x uniformly in time, while p is bounded. Our method is based on a fixed-point theorem which uses the rotational properties of the dynamics.(c) 2022 Elsevier Inc. All rights reserved.

引用

页码：401 / 417

页数：17

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