Multiple Positive Solutions for a Fourth-order p-Laplacian Sturm-Liouville Boundary Value Problems on Time Scales

被引：1

作者：

Youzheng DING ^{[1
,2
]}

Zhongli WEI ^{[1
,2
]}

机构：

[1] School of Mathematics, Shandong University

[2] Department of Mathematics, Shandong Jianzhu University

来源：

Acta Mathematicae Applicatae Sinica | 2015年 / 31卷 / 02期

关键词：

time scales; p-Laplacian equation; positive solution; fixed point theorem;

D O I：

暂无

中图分类号：

O175.8 [边值问题];

学科分类号：

070104 ;

摘要：

In this paper, we investigate the existence of multiple positive solutions for the following fourthorder p-Laplacian Sturm-Liouville boundary value problems on time scales ﹛[φp(u△△(t))u △△= f(t, u(σ(t))), t ∈ [a, b],α0 u(a)- β0u△(a) = 0, γ0 u(σ(b)) + δ0 u△(σ(b)) = 0,α0(φp(u△△))(a)- β0(φp(u△△))△(a) = 0,γ0(φp(u△△))(σ(b)) + δ0(φp(u△△))△(σ(b)) = 0,where φp(s) is the p-Laplacian operator. Under growth conditions on the nonlinearity f some existence results of at least two and three positive solutions for the above problem are obtained by virtue of fixed point theorems on cone. In particular, the nonlinearity f may be both sublinear and superlinear.

引用

页码：287 / 296

页数：10

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