A maximum principle for nonlinear differential inequalities

✍ Scribed by Chung-Fen Lee; Cheh-Chih Yeh

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 220 KB
• Volume: 16
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/s0893-9659(03)80055-1

✦ Synopsis

In this paper, we consider the following nonlinear differential inequality: y(t) {~ (¢(t))' +/(~, ~(t))} < o, (El) where ~p and f satisfy some suitable conditions. Let y(t) be a nontrivial solution of (El). We show that the zeros of y(t) are simple; y(t) and y'(t) have at most finite number of zeros on any compact interval [a, b]. Moreover, we establish some nonlinear maximum principles, which extend some results of Protter and Weinberger.