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Indexed by:Journal Papers

Date of Publication:2015-08-01

Journal:MATHEMATICAL METHODS IN THE APPLIED SCIENCES

Included Journals:EI、SCIE、Scopus

Volume:38

Issue:12

Page Number:2650-2662

ISSN No.:0170-4214

Key Words:Kirchhoff type problems; variational methods; a priori estimates

Abstract:In this paper, we establish the existence and non-existence of positive solutions for p-Kirchhoff type problems with a parameter on R-N without assuming the usual compactness conditions. We show that the p-Kirchhoff type problems have at least one positive solution when the parameter is small, while the p-Kirchhoff type problems have no positive solutions when the parameter is large. Our argument is based on variational methods, monotonicity methods, cut-off functional techniques, and a priori estimates techniques. Copyright (c) 2014 John Wiley & Sons, Ltd.