Existence and multiplicity of positive solutions for one-dimensional p-Laplacian problem with sign-changing weight

被引：0

作者：

Miao, Liangying ^{[1
]}

Xu, Man ^{[2
]}

He, Zhiqian ^{[3
]}

机构：

[1] Qinghai Minzu Univ, Coll Math & Stat, Xining 810007, Peoples R China

[2] Northwest Normal Univ, Dept Math, Lanzhou 730070, Peoples R China

[3] Qinghai Univ, Sch Math & Phys, Xining 810016, Peoples R China

来源：

ELECTRONIC RESEARCH ARCHIVE | 2023年 / 31卷 / 06期

关键词：

p-Laplacian problem; positive solution; multiplicity; bifurcation; sign-changing weight; UNILATERAL GLOBAL BIFURCATION; NODAL SOLUTIONS; BLOW-UP;

D O I：

10.3934/era.2023156

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we show the positive solutions set for one-dimensional p-Laplacian prob-lem with sign-changing weight contains a reversed S-shaped continuum. By figuring the shape of unbounded continuum of positive solutions, we identify the interval of bifurcation parameter in which the p-Laplacian problem has one or two or three positive solutions according to the asymptotic behav-ior of nonlinear term at 0 and oo. The proof of the main result is based upon bifurcation technique.

引用

页码：3086 / 3096

页数：11

共 21 条

[1]

[Anonymous], 2014, ABSTR APPL ANAL, DOI DOI 10.1155/2014/502756

[2] Three positive solutions of N-dimensional p-Laplacian with indefinite weight [J].

Chen, Tianlan ;

Ma, Ruyun .

ELECTRONIC JOURNAL OF QUALITATIVE THEORY OF DIFFERENTIAL EQUATIONS, 2019, (19) :1-14

[3] BIFURCATION AND ONE-SIGN SOLUTIONS OF THE p-LAPLACIAN INVOLVING A NONLINEARITY WITH ZEROS [J].

Dai, Guowei .

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2016, 36 (10) :5323-5345

[4] Unilateral global bifurcation and nodal solutions for the p-Laplacian with sign-changing weight [J].

Dai, Guowei ;

Han, Xiaoling ;

Ma, Ruyun .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2014, 59 (06) :847-862

[5] Unilateral global bifurcation phenomena and nodal solutions for p-Laplacian [J].

Dai, Guowei ;

Ma, Ruyun .

JOURNAL OF DIFFERENTIAL EQUATIONS, 2012, 252 (03) :2448-2468

[6] A HOMOTOPIC DEFORMATION ALONG P OF A LERAY-SCHAUDER DEGREE RESULT AND EXISTENCE FOR (/U'/P-2U')'+F(T,U)=O, U(O)=U(T)=O, P-GREATER-THAN-1 [J].

DELPINO, M ;

ELGUETA, M ;

MANASEVICH, R .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1989, 80 (01) :1-13

[7] GLOBAL BIFURCATION FROM THE EIGENVALUES OF THE P-LAPLACIAN [J].

DELPINO, MA ;

MANASEVICH, RF .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1991, 92 (02) :226-251

[8] Non-Lipschitz heterogeneous reaction with a p-Laplacian operator [J].

Diaz, Jose L. .

AIMS MATHEMATICS, 2021, 7 (03) :3395-3417

[9] Bifurcation problems for the p-Laplacian in R(N) [J].

Drabek, P ;

Huang, YX .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 349 (01) :171-188

[10] Three types of self-similar blow-up for the fourth-order p-Laplacian equation with source [J].

Galaktionov, V. A. .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2009, 223 (01) :326-355

← 1 2 3 →