Slope-changing solutions of elliptic problems on

✍ Scribed by Ugo Bessi

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 724 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2007.04.031

✦ Synopsis

We consider the problemu + F u (x, u) = 0 on R n , where F is a smooth function periodic of period 1 in all its variables. We are going to find a non-degeneracy condition on F for which the following holds. If we are given a sequence of positive integers { Ñi } i∈Z and a sequence {α i } i∈Z of real numbers (the slopes), then we shall find an increasing sequence {Q i } of integers and a solution u which is entire, periodic in (x 2 , . . . , x n ) and which is close to the plane α