scholarly journals Existence of Positive Solutions for a Class of Nonlinear Algebraic Systems

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Yongqiang Du ◽  
Guang Zhang ◽  
Wenying Feng
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Zero Point ◽  
Coefficient Matrix ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Algebraic Systems ◽  
Infinite Point ◽  
Nonlinear Algebraic Systems ◽  
Existence Of Positive Solutions

Based on Guo-Krasnoselskii’s fixed point theorem, the existence of positive solutions for a class of nonlinear algebraic systems of the formx=GFxis studied firstly, whereGis a positiven×nsquare matrix,x=col⁡(x1,x2,…,xn), andF(x)=col⁡(f(x1),f(x2),…,f(xn)), where,F(x)is not required to be satisfied sublinear or superlinear at zero point and infinite point. In addition, a new cone is constructed inRn. Secondly, the obtained results can be extended to some more general nonlinear algebraic systems, where the coefficient matrixGand the nonlinear term are depended on the variablex. Corresponding examples are given to illustrate these results.

scholarly journals Existence of Positive Solutions for Fourth-Order Boundary Value Problems with Sign-Changing Nonlinear Terms

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Xingfang Feng ◽  
Hanying Feng
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Fourth Order ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

the existence of positive solutions for a fourth-order boundary value problem with a sign-changing nonlinear term is investigated. By using Krasnoselskii’s fixed point theorem, sufficient conditions that guarantee the existence of at least one positive solution are obtained. An example is presented to illustrate the application of our main results.

scholarly journals Positive Solutions of a Fractional Boundary Value Problem with Changing Sign Nonlinearity

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Yongqing Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Fractional Differential

We discuss the existence of positive solutions of a boundary value problem of nonlinear fractional differential equation with changing sign nonlinearity. We first derive some properties of the associated Green function and then obtain some results on the existence of positive solutions by means of the Krasnoselskii's fixed point theorem in a cone.

scholarly journals Existence of positive solutions to BVPs of higher order delay differential equations

2009 ◽  
Vol 42 (1) ◽  
Author(s):  
Jianhua Shen ◽  
Jing Dong
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Delay Differential Equations ◽  
Nonlinear Eigenvalue Problem ◽  
Higher Order ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Semipositone Problem ◽  
Delay Differential

AbstractThe paper is concerned with the existence of positive solutions for the nonlinear eigenvalue problem with singularity and the superlinear semipositone problem of higher order delay differential equations. The main results are obtained by using Guo-Krasnoselskii’s fixed point theorem in cones. These results extend some of the existing literature.

scholarly journals The boundary value problem of higher order differential equations with delay

2013 ◽  
Vol 46 (1) ◽  
Author(s):  
Zhimin He ◽  
Jianhua Shen
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
Equations With Delay ◽  
Higher Order Differential Equations

AbstractIn the paper, Guo–Krasnoselskii’s fixed point theorem is adapted to study the existence of positive solutions to a class of boundary value problems for higher order differential equations with delay. The sufficient conditions, which assure that the equation has one positive solution or two positive solutions, are derived. These conclusions generalize some existing ones.

scholarly journals Positive Solutions for Second-Order Singular Semipositone Differential Equations Involving Stieltjes Integral Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Second Order ◽  
Stieltjes Integral ◽  
Integral Conditions ◽  
Existence Of Positive Solutions

By means of the fixed point theory in cones, we investigate the existence of positive solutions for the following second-order singular differential equations with a negatively perturbed term:−u′′(t)=λ[f(t,u(t))−q(t)],0<t<1,αu(0)−βu′(0)=∫01u(s)dξ(s),γu(1)+δu′(1)=∫01u(s)dη(s),whereλ>0is a parameter;f:(0,1)×(0,∞)→[0,∞)is continuous;f(t,x)may be singular att=0,t=1,andx=0, and the perturbed termq:(0,1)→[0,+∞)is Lebesgue integrable and may have finitely many singularities in(0,1), which implies that the nonlinear term may change sign.

scholarly journals Positive solutions of functional-differential systems via the vector version of Krasnoselskii’s fixed point theorem in cones

2011 ◽  
Vol 27 (2) ◽  
pp. 165-172
Author(s):  
SORIN BUDISAN ◽  
◽  
RADU PRECUP ◽  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Point Theorem ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Functional Differential Systems ◽  
Existence Of Positive Solutions ◽  
Vector Version ◽  
Functional Differential ◽  
Functional Differential System

We study the existence of positive solutions of the functional-differential system ... (0 < t < 1), subject to linear boundary conditions. We prove the existence of at least one positive solution by using the vector version of Krasnoselskii’s fixed point theorem in cones.

scholarly journals Positive Solutions to a Generalized Second-Order Difference Equation with Summation Boundary Value Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-15
Author(s):  
Thanin Sitthiwirattham ◽  
Jessada Tariboon
Keyword(s):  
Fixed Point ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Order Difference ◽  
Existence Of Positive Solutions ◽  
Second Order Difference Equation ◽  
Order Difference Equation ◽  
Fixed Positive Integer

By using Krasnoselskii's fixed point theorem, we study the existence of positive solutions to the three-point summation boundary value problemΔ2u(t-1)+a(t)f(u(t))=0,t∈{1,2,…,T},u(0)=β∑s=1ηu(s),u(T+1)=α∑s=1ηu(s), wherefis continuous,T≥3is a fixed positive integer,η∈{1,2,...,T-1},0<α<(2T+2)/η(η+1),0<β<(2T+2-αη(η+1))/η(2T-η+1),andΔu(t-1)=u(t)-u(t-1). We show the existence of at least one positive solution iffis either superlinear or sublinear.

scholarly journals Positive Solutions of a Singular Positone and Semipositone Boundary Value Problems for Fourth-Order Difference Equations

2010 ◽  
Vol 2010 ◽  
pp. 1-16 ◽  
Author(s):  
Chengjun Yuan
Keyword(s):  
Fixed Point ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Fourth Order ◽  
Difference Equations ◽  
Fixed Point Theorems ◽  
Nonlinear Term ◽  
Boundary Value ◽  
Order Difference ◽  
Existence Of Positive Solutions

This paper studies the boundary value problems for the fourth-order nonlinear singular difference equationsΔ4u(i−2)=λα(i)f(i,u(i)),i∈[2,T+2],u(0)=u(1)=0,u(T+3)=u(T+4)=0. We show the existence of positive solutions for positone and semipositone type. The nonlinear term may be singular. Two examples are also given to illustrate the main results. The arguments are based upon fixed point theorems in a cone.

scholarly journals Exact Multiplicity of Solutions for a Class of Singular Generalized One-Dimensionalp-Laplacian Problem

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Youwei Zhang
Keyword(s):  
Fixed Point ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Point Theory ◽  
One Dimensional ◽  
First Order ◽  
Existence Of Positive Solutions ◽  
Exact Multiplicity Of Solutions ◽  
Exact Multiplicity

We describe the existence of positive solutions for a class of singular generalized one-dimensionalp-Laplacian problem. By applying the related fixed point theory in cone, some new and general results on the existence of positive solutions to the singular generalizedp-Laplacian problem are obtained. Note that the nonlinear termfinvolves the first-order derivative explicitly.

Positive solutions of a discrete nonlinear third-order three-point eigenvalue problem with sign-changing Green's function

2021 ◽  
Vol 19 (1) ◽  
pp. 990-1006
Author(s):  
Xueqin Cao ◽  
Chenghua Gao ◽  
Duihua Duan
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Positive Solutions ◽  
Existence Results ◽  
Point Boundary ◽  
Third Order ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions ◽  
The Green Function

Abstract In this paper, we discuss the existence of positive solutions to a discrete third-order three-point boundary value problem. Here, the weight function a ( t ) a\left(t) and the Green function G ( t , s ) G\left(t,s) both change their sign. Despite this, we also obtain several existence results of positive solutions by using the Guo-Krasnoselskii’s fixed-point theorem in a cone.

Sign in / Sign up

Export Citation Format

Share Document