POSITIVE SOLUTIONS OF ONE-DIMENSIONAL p-LAPLACIAN EQUATIONS AND APPLICATIONS TO POPULATION MODELS OF ONE SPECIES

被引：2

作者：

Lan, Kunquan ^{[1
]}

Yang, Xiaojing ^{[2
]}

Yang, Guangchong ^{[3
]}

机构：

[1] Ryerson Univ, Dept Math, Toronto, ON M5B 2K3, Canada

[2] Tsinghua Univ, Dept Math Sci, Beijing 100084, Peoples R China

[3] Chengdu Univ Informat Technol, Coll Math, Chengdu 610225, Sichuan, Peoples R China

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2015年 / 46卷 / 01期

基金：

中国国家自然科学基金; 加拿大自然科学与工程研究理事会;

关键词：

One-dimensional p-Laplacian equations; positive solutions; sublinear condition; fixed point index; logistic population model; SIGN-CHANGING SOLUTIONS; BOUNDARY-VALUE-PROBLEMS; STRONG SINGULAR WEIGHT; NONUNIFORM NONRESONANCE; NONLINEAR EQUATIONS; EIGENVALUE CRITERIA; EXISTENCE; MULTIPLICITY; BIFURCATION; SYSTEMS;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove new results on the existence of positive solutions of one-dimensional p-Laplacian equations under sublinear conditions involving the first eigenvalues of the corresponding homogeneous Dirichlet boundary value problems. To the best of our knowledge, this is the first paper to use fixed point index theory of compact maps to give criteria involving the first eigenvalue for one-dimensional p-Laplacian equations with p not equal 2. Our results generalize some previous results where either p is required to be greater than 2 or the nonlinearities satisfy stronger conditions. We shall apply our results to tackle a logistic population model arising in mathematical biology.

引用

页码：431 / 445

页数：15

共 41 条

[1] Eigenvalues and the one-dimensional p-Laplacian [J].