scholarly journals Multiplicity of Positive Solutions for a Singular Second-Order Three-Point Boundary Value Problem with a Parameter

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Jian Liu ◽  
Hanying Feng ◽  
Xingfang Feng
Keyword(s):  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Point Boundary ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

This paper is concerned with the following second-order three-point boundary value problemu″t+β2ut+λqtft,ut=0,t∈0 , 1,u0=0,u(1)=δu(η), whereβ∈(0,π/2),δ>0,η∈(0,1), andλis a positive parameter. First, Green’s function for the associated linear boundary value problem is constructed, and then some useful properties of Green’s function are obtained. Finally, existence, multiplicity, and nonexistence results for positive solutions are derived in terms of different values ofλby means of the fixed point index theory.

scholarly journals Positive Solutions for a Mixed-Order Three-Point Boundary Value Problem forp-Laplacian

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Francisco J. Torres
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Main Tool ◽  
Index Theory ◽  
Laplacian Operator ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

The author investigates the existence and multiplicity of positive solutions for boundary value problem of fractional differential equation withp-Laplacian operator. The main tool is fixed point index theory and Leggett-Williams fixed point theorem.

scholarly journals Positive Solutions of a Third-Order Three-Point BVP with Sign-Changing Green’s Function

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Li-Juan Gao ◽  
Jian-Ping Sun
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Green’S Function ◽  
Positive Solutions ◽  
Green's Function ◽  
Point Theorem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order

We are concerned with the following third-order three-point boundary value problem:u′′′t=ft, ut,   t∈0, 1,   u′0=u1=0and u′′η-αu′1=0,whereα∈0, 1andη∈(14+α)/(24-3α),1. Although the corresponding Green’s function is sign-changing, we still obtain the existence of at least two positive and decreasing solutions under some suitable conditions onfby using the two-fixed-point theorem due to Avery and Henderson.

scholarly journals Positive Solutions for a Fourth-Order Boundary Value Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-8
Author(s):  
Kun Wang ◽  
Zhilin Yang
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
A Priori Estimates ◽  
Boundary Value ◽  
A Priori ◽  
Index Theory ◽  
Existence And Multiplicity ◽  
Fixed Point Index Theory ◽  
Multiplicity Of Positive Solutions

This paper deals with the existence and multiplicity of positive solutions for the fourth-order boundary value problemu(4)=f(t,u,u′,−u′′, u′′′),u(0)=u′(1)=u′′′(0)=u′′(1)=0. Heref∈C([0,1]×ℝ+4,ℝ+)(ℝ+:=[0,+∞)). We use fixed point index theory to establish our main results based on a priori estimates achieved by utilizing some integral identities and integral inequalities.

scholarly journals Positive solutions of a discrete second-order boundary value problems with fully nonlinear term

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Liyun Jin ◽  
Hua Luo
Keyword(s):  
Positive Solutions ◽  
Fixed Point Index ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Index Theory ◽  
Second Order ◽  
Fully Nonlinear ◽  
Fixed Point Index Theory ◽  
Weaker Conditions ◽  
Lower Limits

Abstract In this paper, we mainly consider a kind of discrete second-order boundary value problem with fully nonlinear term. By using the fixed-point index theory, we obtain some existence results of positive solutions of this kind of problems. Instead of the upper and lower limits condition on f, we may only impose some weaker conditions on f.

Sign in / Sign up

Export Citation Format

Share Document