Electron. J. Differential Equations, Vol. 2017 (2017), No. 107, pp. 1-37.

Bifurcation of positive solutions for the one-dimensional (p,q)-Laplace equation

Ryuji Kajikiya, Mieko Tanaka, Satoshi Tanaka

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
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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