Positive solutions for p‐Kirchhoff type problems on
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| Authors: | Xiyou Cheng Guowei Dai |
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| Affiliation: | 1. School of Mathematics and Statistics, Lanzhou University, Lanzhou, China;2. Key Laboratory of Applied Mathematics and Complex Systems, Gansu, China;3. School of Mathematical Sciences, Dalian University of Technology, Dalian, China |
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| Abstract: | In this paper, we establish the existence and non‐existence of positive solutions for p‐Kirchhoff type problems with a parameter on  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 © 2014 John Wiley & Sons, Ltd. |
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| Keywords: | Kirchhoff type problems variational methods a priori estimates |
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