Positive entire solutions to nonlinear biharmonic equations in the plane

✍ Scribed by Yasuhiro Furusho; Kusano Takaŝi

• Publisher: Elsevier Science
• Year: 1998
• Tongue: English
• Weight: 531 KB
• Volume: 88
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(97)00214-8

✦ Synopsis

Two-dimensional nonlinear biharmonic equations of the form

are considered, where p > 1 is a constant and f : R+ x R+ --* R+ is a continuous function. It can be shown that any positive radially symmetric solution is unbounded and grows at least as fast as positive constant multiples of [x]2(log[xD 1/(p-1) as [x[ --+ (x3. In this paper sharp conditions on f are presented under which (*) has infinitely many positive symmetric entire solutions which are asymptotic to positive constant multiples of Ixl2(loglxD v(p-1) as Ixl ~ oo.