Ryuji Kajikiya, Mieko Tanaka, Satoshi Tanaka
Abstract:
In this article, we study the bifurcation of positive solutions for
the one-dimensional (p,q)-Laplace equation under Dirichlet boundary
conditions. We investigate the shape of the bifurcation diagram
and prove that there exist five different types of bifurcation diagrams.
As a consequence, we prove the existence of multiple positive solutions and
show the uniqueness of positive solutions for a bifurcation parameter in
a certain range.
Submitted February 8, 2017. Published April 21, 2017.
Math Subject Classifications: 34B09, 34B18, 34C23, 34L30.
Key Words: Bifurcation; positive solution; (p,q)-Laplace equation; time map;
multiple solutions.
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| Ryuji Kajikiya Department of Mathematics Faculty of Science and Engineering Saga University, Saga 840-8502, Japan email: kajikiya@ms.saga-u.ac.jp | |
| Mieko Tanaka Department of Mathematics Tokyo University of Science Kagurazaka 1-3, Shinjyuku-ku Tokyo 162-8601, Japan email: miekotanaka@rs.tus.ac.jp | |
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Satoshi Tanaka Department of Applied Mathematics Faculty of Science Okayama University of Science Okayama 700-005, Japan email: tanaka@xmath.ous.ac.jp |
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