A complete classification of bifurcation diagrams for a class of (p,q)-Laplace equations

Ryuji Kajikiya, Inbo Sim, Satoshi Tanaka

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We study the bifurcation problem of positive solutions for the one-dimensional (p,q)-Laplace equation with nonlinear term ur−1. There are five types of order relations for (p,q,r). We investigate the exact shape of the bifurcation curve in each type of the order relation. We prove that there are two types of bifurcation curves that are increasing, two types that are decreasing, and one that is not monotone and turns exactly once. Moreover, we study the asymptotic profile of the normalized solution u(x)/‖u‖ as ‖u‖→0 or ‖u‖→∞ where ‖u‖ denotes the L-norm of u.

Original languageEnglish
Pages (from-to)1178-1194
Number of pages17
JournalJournal of Mathematical Analysis and Applications
Volume462
Issue number2
DOIs
Publication statusPublished - 2018 Jun 15
Externally publishedYes

Keywords

  • (p,q)-Laplace equation
  • Bifurcation
  • Multiple solutions
  • Positive solution
  • Time map

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Fingerprint Dive into the research topics of 'A complete classification of bifurcation diagrams for a class of (p,q)-Laplace equations'. Together they form a unique fingerprint.

Cite this