Existence of critical point for abstract resonant problems with unbounded nonlinearities and applications to differential equations

✍ Scribed by Qingdong Li; Zhi-Qing Han

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 224 KB
• Volume: 65
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2005.10.047

✦ Synopsis

In this paper, using well-known variational methods, we prove a general abstract theorem on the existence of a critical point for resonant problems with unbounded nonlinearities and then apply it to ordinary and partial differential equations with generalized Ahmad-Lazer-Paul conditions. The abstract result contains several concrete results in the literature and can also be used to deal with some new cases for resonant differential equations.