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.

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 Triple positive solutions for the one-dimensional $p$-laplacian

2006 ◽  
Vol 37 (1) ◽  
pp. 15-25
Author(s):  
Zhanbing Bai ◽  
Mingfu Ma ◽  
Xiangqian Liang
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Sufficient Conditions ◽  
One Dimensional ◽  
First Order ◽  
Triple Positive Solutions ◽  
The One

We consider the boundary value problem: $ \left(\varphi_p(x'(t))\right)'+ q(t)f(t, x(t), x'(t))=0, p>1, t \in [0, 1] $, with $ x(0)=x(1)=0 $, or $ x(0)=x'(1)=0 $. Using a fixed point theorem due to Avery and Peterson, sufficient conditions are obtained that guarantee the existence of at least three positive solutions. The emphasis here is the nonlinear term $ f $ is involved with the first order derivative. An example is also included to illustrate the importance of the results obtained

scholarly journals Positive Solutions forp-Laplacian Fourth-Order Differential System with Integral Boundary Conditions

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jiqiang Jiang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Boundary Conditions ◽  
Positive Solutions ◽  
Fourth Order ◽  
Fixed Point Theory ◽  
Integral Boundary Conditions ◽  
Point Theory ◽  
Integral Boundary ◽  
Value System ◽  
Existence Of Positive Solutions

This paper investigates the existence of positive solutions for a class of singularp-Laplacian fourth-order differential equations with integral boundary conditions. By using the fixed point theory in cones, explicit range forλandμis derived such that for anyλandμlie in their respective interval, the existence of at least one positive solution to the boundary value system is guaranteed.

scholarly journals Application of Fixed-Point Theory for a Nonlinear Fractional Three-Point Boundary-Value Problem

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 526
Author(s):  
Ehsan Pourhadi ◽  
Reza Saadati ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Point Theorem ◽  
Fixed Point Theory ◽  
Boundary Value ◽  
Point Theory ◽  
Point Boundary ◽  
Krasnoselskii’S Fixed Point Theorem ◽  
Existence Of Positive Solutions

Throughout this paper, via the Schauder fixed-point theorem, a generalization of Krasnoselskii’s fixed-point theorem in a cone, as well as some inequalities relevant to Green’s function, we study the existence of positive solutions of a nonlinear, fractional three-point boundary-value problem with a term of the first order derivative ( a C D α x ) ( t ) = f ( t , x ( t ) , x ′ ( t ) ) , a < t < b , 1 < α < 2 , x ( a ) = 0 , x ( b ) = μ x ( η ) , a < η < b , μ > λ , where λ = b − a η − a and a C D α denotes the Caputo’s fractional derivative, and f : [ a , b ] × R × R → R is a continuous function satisfying the certain conditions.

scholarly journals A Constructive Approach About the Existence of Positive Solutions for Minkowski Curvature Problems

2021 ◽  
Author(s):  
Rui Yang ◽  
Jong Kyu Lee ◽  
Yong-Hoon Lee
Keyword(s):  
Existence Theorem ◽  
Positive Solutions ◽  
Nonlinear Term ◽  
Numerical Range ◽  
Parameter Family ◽  
Constructive Method ◽  
Coefficient Function ◽  
One Dimensional ◽  
Existence Of Positive Solutions ◽  
Cone Expansion And Compression

AbstractIn this paper, we give an existence theorem about positive solutions for the Dirichlet boundary value problem of one dimensional Minkowski curvature equations. We apply the theorem to one parameter family of problems to investigate a constructive method for numerical range of parameters where positive solutions exist. Moreover, we establish a nonexistence theorem of positive solutions for the corresponding one parameter family of problems. The coefficient function may be singular at the boundary and nonlinear term satisfies a sublinear growth condition. Main argument for the proof of existence theorem is employed by Krasnoselskii’s theorem of cone expansion and compression. We give a numerical algorithm and various examples to illustrate numerical information about ranges of the existence and nonexistence parameters which have been given only in a theoretical manner so far.

scholarly journals Existence Theory for Pseudo-Symmetric Solution to -Laplacian Differential Equations Involving Derivative

2011 ◽  
Vol 2011 ◽  
pp. 1-19
Author(s):  
You-Hui Su ◽  
Weili Wu ◽  
Xingjie Yan
Keyword(s):  
Differential Equation ◽  
Fixed Point ◽  
Boundary Value Problem ◽  
Symmetric Solution ◽  
Nonlinear Term ◽  
Fixed Point Theory ◽  
Sufficient Conditions ◽  
Point Theory ◽  
Existence Theory ◽  
Point Boundary

We all-sidedly consider a three-point boundary value problem for -Laplacian differential equation with nonlinear term involving derivative. Some new sufficient conditions are obtained for the existence of at least one, triple, or arbitrary odd positive pseudosymmetric solutions by using pseudosymmetric technique and fixed-point theory in cone. As an application, two examples are given to illustrate the main results.

scholarly journals Some Notes on the Existence of Solution for Ordinary Differential Equations via Fixed Point Theory

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Fei He
Keyword(s):  
Fixed Point ◽  
Metric Spaces ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Lower Solution ◽  
Existence Of Solution ◽  
Order Ordinary Differential Equation ◽  
Complete Metric Spaces ◽  
First Order ◽  
Contractive Mappings

We establish a fixed point theorem withw-distance for nonlinear contractive mappings in complete metric spaces. As applications of our results, we derive the existence and uniqueness of solution for a first-order ordinary differential equation with periodic boundary conditions. Here, we need not assume that the equation has a lower solution.

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 Positive Solutions for Discrete Boundary Value Problems to One-Dimensionalp-Laplacian with Delay

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Linjun Wang ◽  
Xumei Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Numerical Examples ◽  
One Dimensional ◽  
Existence Of Positive Solutions ◽  
Krasnoselskii Fixed Point Theorem ◽  
Theoretical Results

We study the existence of positive solutions for discrete boundary value problems to one-dimensionalp-Laplacian with delay. The proof is based on the Guo-Krasnoselskii fixed-point theorem in cones. Two numerical examples are also provided to illustrate the theoretical results.

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