Baoqiang Yan, Donal O'Regan, Ravi P. Agarwal
Abstract:
This article considers elliptic problems of Kirchhoff-type. We
give some new definitions of lower and upper solutions for the problem and establish
the method of lower and upper solutions when the upper and lower solutions are well
ordered, i.e., the lower solution is less than the upper one, and we also
consider the case when the upper and lower solutions have opposite ordering.
In addition we use the relation between the topological degree and strict upper
and lower solutions in both cases and using this we obtain multiplicity results for
nonlinear Kirchhoff-type elliptic problems.
Submitted January 31, 2019. Published April 29, 2019.
Math Subject Classifications: 35J60, 35J75, 47H10.
Key Words: Kirchhoff-type elliptic problem; lower and upper solution;
topological degree.
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Baoqiang Yan School of Mathematical Sciences Shandong Normal University Jinan, 250014, China email: yanbqcn@aliyun.com |
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Donal O'Regan School of Mathematics, Statistics and Applied Mathematics National University of Ireland Galway, Ireland email: donal.oregan@nuigalway.ie |
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Ravi P. Agarwal Department of Mathematics Texas A and M University-Kingsville Texas 78363, USA email: Ravi.Agarwal@tamuk.edu |
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