Weak and strong solutions for differential equations in Banach spaces

✍ Scribed by A.M. Gomaa

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 111 KB
• Volume: 18
• Category: Article
• ISSN: 0960-0779
• DOI: 10.1016/s0960-0779(02)00643-4

✦ Synopsis

In this paper we give a generalization to recent results by using weak and strong measures of noncompactness. For f : ½0; T Â E ! E with E is a Banach space we prove that, under suitable assumptions, the Cauchy problem

has at least one weak solution furthermore, with certain conditions, the Cauchy problem ðP Þ has a solution. Next under a generalization of the compactness assumptions, we show that ðP Þ has a solution too.