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Positive solutions for p ‐Kirchhoff type problems on R N
Author(s) -
Cheng Xiyou,
Dai Guowei
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3396
Subject(s) - mathematics , monotonic function , type (biology) , compact space , a priori and a posteriori , mathematical analysis , kirchhoff integral theorem , differential equation , ecology , philosophy , epistemology , summation equation , biology
In this paper, we establish the existence and non‐existence of positive solutions for p ‐Kirchhoff type problems with a parameter onR Nwithout 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 © 2014 John Wiley & Sons, Ltd.