Remarks on the periodic boundary value problems for first-order differential equations

✍ Scribed by Zhuang Wan; Yubo Chen; Jie Chen

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 320 KB
• Volume: 37
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/s0898-1221(99)00100-5

✦ Synopsis

Abstrac',, This paper is concerned with the existence of solutions and the monotone method of first-order periodic boundary value problems when the lower and upper solutions c~ and B violate the boundary conditions a(0) _< a(21r) and ~(0) _~ ~(21r). Using the topological degree theory, two existence theorems are established under weaker conditions than the one-side Lipschitz conditions. An example is given, which illustrates that PBVP may not have solutions between c~ and/~ without further restrictions to f(t, u). The monotone method is also discussed with some new results. (~) 1999 Elsevier Science Ltd. All rights reserved.