One-Sided Resonance Problems for Quasilinear Elliptic Operators

✍ Scribed by Stephen B. Robinson; Adolfo J. Rumbos; Victor L. Shapiro

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 123 KB
• Volume: 256
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2000.7333

✦ Synopsis

We present some new existence results for a quasilinear elliptic problem with an unbounded driving force. The quasilinear elliptic operator is assumed to be variational and is such that 0 acts like an isolated eigenvalue with a corresponding eigenfunction which does not change sign. The driving force is further assumed to be in one-sided resonance around the eigenvalue 0, and a solvability condition of potential type is imposed. Variational methods are used to obtain existence. Our results significantly improve earlier results of the authors.