TY - JOUR

T1 - A complete classification of bifurcation diagrams for a class of (p,q)-Laplace equations

AU - Kajikiya, Ryuji

AU - Sim, Inbo

AU - Tanaka, Satoshi

N1 - Funding Information:
The third author was supported by JSPS KAKENHI Grant Number 26400182.
Publisher Copyright:
© 2018 Elsevier Inc.

PY - 2018/6/15

Y1 - 2018/6/15

N2 - 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.

AB - 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.

KW - (p,q)-Laplace equation

KW - Bifurcation

KW - Multiple solutions

KW - Positive solution

KW - Time map

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U2 - 10.1016/j.jmaa.2018.02.049

DO - 10.1016/j.jmaa.2018.02.049

M3 - Article

AN - SCOPUS:85042686459

VL - 462

SP - 1178

EP - 1194

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -