Quasilinear Problems Involving Changing-Sign Nonlinearities without an Ambrosetti–Rabinowitz-Type Condition. Issue 3 (October 2014)

• Record Type: Journal Article
• Authors: Iturriaga, Leonelo; Souto, Marco A.; Ubilla, Pedro
• Is Part Of: Proceedings of the Edinburgh Mathematical Society. Volume 57:Issue 3(2014)
• Page Start: 755
• Page End: 762
• Publication Date: 2014-10
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1017/S0013091513000667
• Languages: English
• ISSNs: 0013-0915

Abstract

<abstract abstract-type="normal"> <title>Abstract</title> <p>In this paper quasilinear elliptic boundary value equations without an Ambrosetti and Rabinowitz growth condition are considered. Existence of a non-trivial solution result is established. For this, we show the existence of a Cerami sequence by using a variant of the mountain-pass theorem due to Schechter. The novelty here is that we may consider nonlinearities that satisfy a local <italic>p</italic>-superlinear condition and may change sign.</p> </abstract>