Superlinear Equations Involving Nonlinearities Limited by Asymptotically Homogeneous Functions. (17th May 2007)

• Record Type: Journal Article
• Authors: Lorca, Sebastián; Souto, Marco Aurelio; Ubilla, Pedro
• Other Names: Giga Y. Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2007(2007)
• Publication Date: 2007-05-17
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2007/58363
• Languages: English
• ISSNs: 1029-242X

Abstract

Abstract : We obtain a solution of the quasilinear equation− Δ p u = f ( u ) inΩ, u = 0, on∂ Ω . Here the nonlinearityf is superlinear at zero, and it is located near infinity between two functions that belong to a class of functions where the Ambrosetti-Rabinowitz condition is satisfied. More precisely, we consider the class of functions that are asymptotically homogeneous of indexq .