NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS

被引：0

作者：

赵增勤 ^{[1
]}

机构：

[1] School of Mathematical Sciences, Qufu Normal University

来源：

Acta Mathematica Scientia | 2011年 / 31卷 / 04期

基金：

中国国家自然科学基金;

关键词：

2nth-order differential equation; singular boundary value problem; fixed point theorem; positive solution;

D O I：

暂无

中图分类号：

O175.8 [边值问题];

学科分类号：

摘要：

This paper investigates a class of 2nth-order singular superlinear problems with Strum-Liouville boundary conditions. We obtain a necessary and sufficient condition for the existence of C 2 n- 2 [0, 1] positive solutions, and a sufficient condition, a necessary condition for the existence of C 2 n-1 [0, 1] positive solutions. Relations between the positive solutions and the Green’s functions are depicted. The results are used to judge nonexistence or existence of positive solutions for given boundary value problems.

引用

页码：1569 / 1582

页数：14

共 50 条

[1] NONEXISTENCE AND EXISTENCE OF POSITIVE SOLUTIONS FOR 2nTH-ORDER SINGULAR SUPERLINEAR PROBLEMS WITH STRUM-LIOUVILLE BOUNDARY CONDITIONS
Zhao Zengqin
ACTA MATHEMATICA SCIENTIA, 2011, 31 (04) : 1569 - 1582
[2] Existence of positive solutions for 2nth-order singular superlinear boundary value problems
Cui, Yujun
Zou, Yumei
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2008, 56 (12) : 3195 - 3203
[3] Existence of positive solutions for 2nth-order singular sublinear boundary value problems
Wei, ZL
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 306 (02) : 619 - 636
[4] Existence of positive solutions for 2nth-order singular semipositone differential equations with Sturm-Liouville boundary conditions
Zhao, Zengqin
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2010, 72 (3-4) : 1348 - 1357
[5] Positive solutions for a class of 2nth-order singular boundary value problems
Zhang, Xuemei
Feng, Meiqiang
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (04) : 1287 - 1298
[6] ON THE EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR 2nTH-ORDER BOUNDARY VALUE PROBLEMS
Pei Minghe (Dept. of Math.
Annals of Differential Equations, 2005, (02) : 183 - 191
[7] A class of 2nth-order singular boundary value problems
Wei, Zhongli
Pang, Changci
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (06) : 1225 - 1245
[8] Existence and Uniquenes Theorems of Solutions for a Class of 2nth-order Boundary Value Problems
Pei Minghe (Department of Mathematics
Northeastern Mathematical Journal, 1999, (01) : 121 - 126
[9] Existence of positive solutions of fourth-order singular superlinear boundary value problems
Shi, GL
Chen, SZ
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 2003, 34 (07): : 997 - 1012
[10] NONEXISTENCE AND EXISTENCE RESULTS FOR A 2nth-ORDER DISCRETE DIRICHLET BOUNDARY VALUE PROBLEM
Shi, Haiping
Liu, Xia
Zhang, Yuanbiao
KODAI MATHEMATICAL JOURNAL, 2014, 37 (02) : 492 - 505

← 1 2 3 4 5 →