Positive solutions for some boundary value problems via a new fixed point theorem

Positivity ◽  
2014 ◽  
Vol 19 (3) ◽  
pp. 587-602 ◽  
Author(s):  
Sana Hadj Amor
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value

scholarly journals Blow-Up Solutions for a Singular Nonlinear Hadamard Fractional Boundary Value Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Imed Bachar ◽  
Said Mesloub
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Blow Up ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Fractional Boundary Value Problems

We consider singular nonlinear Hadamard fractional boundary value problems. Using properties of Green’s function and a fixed point theorem, we show that the problem has positive solutions which blow up. Finally, some examples are provided to explain the applications of the results.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR SUPERLINEAR SEMIPOSITONE $m$-POINT BOUNDARY-VALUE PROBLEMS

2003 ◽  
Vol 46 (2) ◽  
pp. 279-292 ◽  
Author(s):  
Ruyun Ma
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Positive Parameter ◽  
Point Boundary ◽  
Existence Of Positive Solutions ◽  
The Fixed Point Theorem

AbstractIn this paper we consider the existence of positive solutions to the boundary-value problems\begin{align*} (p(t)u')'-q(t)u+\lambda f(t,u)\amp=0,\quad r\ltt\ltR, \\[2pt] au(r)-bp(r)u'(r)\amp=\sum^{m-2}_{i=1}\alpha_iu(\xi_i), \\ cu(R)+dp(R)u'(R)\amp=\sum^{m-2}_{i=1}\beta_iu(\xi_i), \end{align*}where $\lambda$ is a positive parameter, $a,b,c,d\in[0,\infty)$, $\xi_i\in(r,R)$, $\alpha_i,\beta_i\in[0,\infty)$ (for $i\in\{1,\dots m-2\}$) are given constants satisfying some suitable conditions. Our results extend some of the existing literature on superlinear semipositone problems. The proofs are based on the fixed-point theorem in cones.AMS 2000 Mathematics subject classification: Primary 34B10, 34B18, 34B15

Positive solutions of superlinear boundary value problems

1981 ◽  
Vol 88 (1-2) ◽  
pp. 17-24 ◽  
Author(s):  
Heinrich Voss
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Of Positive Solutions ◽  
Image Position

SynopsisUsing a fixed point theorem on operators expanding a cone in a Banach space we prove the existence of positive solutions of superlinear boundary value problemsAt the same time we get bounds (or even inclusions) of positive solutions.

scholarly journals Triple Positive Solutions for Third-Orderm-Point Boundary Value Problems on Time Scales

2009 ◽  
Vol 2009 ◽  
pp. 1-15
Author(s):  
Jian Liu ◽  
Fuyi Xu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Point Boundary ◽  
Third Order ◽  
Triple Positive Solutions

We study the following third-orderm-point boundary value problems on time scales(φ(uΔ∇))∇+a(t)f(u(t))=0,t∈[0,T]T,u(0)=∑i=1m−2biu(ξi),uΔ(T)=0,φ(uΔ∇(0))=∑i=1m−2ciφ(uΔ∇(ξi)), whereφ:R→Ris an increasing homeomorphism and homomorphism andφ(0)=0,0<ξ1<⋯<ξm−2<ρ(T). We obtain the existence of three positive solutions by using fixed-point theorem in cones. The conclusions in this paper essentially extend and improve the known results.

scholarly journals Multiple positive solutions of Strum-Liouville equations with singularities

2006 ◽  
Vol 2006 ◽  
pp. 1-11 ◽  
Author(s):  
Zenggui Wang ◽  
Lishan Liu ◽  
Yonghong Wu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Multiple Positive Solutions ◽  
Multiplicity Results ◽  
Existence And Multiplicity

The existence of multiple positive solutions for Strum-Liouville boundary value problems with singularities is investigated. By applying a fixed point theorem of cone map, some existence and multiplicity results of positive solutions are derived. Our results improve and generalize those in some well-known results.

scholarly journals Existence of Three Positive Solutions for a Class of Boundary Value Problems of Caputo Fractional q-Difference Equation

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Huiqin Chen ◽  
Shugui Kang ◽  
Lili Kong ◽  
Ying Gao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Difference Equation ◽  
Green’S Function ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Green's Function ◽  
Point Theorem ◽  
Boundary Value ◽  
Existence Criteria

A class of boundary value problems of Caputo fractional q-difference equation is introduced. Green’s function and its properties for this problem are deduced. By applying these properties and the Leggett-Williams fixed-point theorem, existence criteria of three positive solutions are obtained. At last, some examples are given to illustrate the validity of our main results.

scholarly journals Existence of Three Positive Solutions form-Point Discrete Boundary Value Problems withp-Laplacian

2009 ◽  
Vol 2009 ◽  
pp. 1-15 ◽  
Author(s):  
Yanping Guo ◽  
Wenying Wei ◽  
Yuerong Chen
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Laplacian Operator ◽  
One Dimensional

We consider the multi-point discrete boundary value problem with one-dimensionalp-Laplacian operatorΔ(ϕp(Δu(t−1))+q(t)f(t,u(t),Δu(t))=0,t∈{1,…,n−1}subject to the boundary conditions:u(0)=0,u(n)=∑i=1m−2aiu(ξi), whereϕp(s)=|s|p−2s,p>1,ξi∈{2,…,n−2}with1<ξ1<⋯<ξm−2<n−1andai∈(0,1),0<∑i=1m−2ai<1. Using a new fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem.

scholarly journals Existence of Triple Positive Solutions for Second-Order Discrete Boundary Value Problems

2007 ◽  
Vol 2007 ◽  
pp. 1-10 ◽  
Author(s):  
Yanping Guo ◽  
Jiehua Zhang ◽  
Yude Ji
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Second Order ◽  
Triple Positive Solutions

By using a new fixed-point theorem introduced by Avery and Peterson (2001), we obtain sufficient conditions for the existence of at least three positive solutions for the equationΔ2x(k−1)+q(k)f(k,x(k),Δx(k))=0, fork∈{1,2,…,n−1}, subject to the following two boundary conditions:x(0)=x(n)=0orx(0)=Δx(n−1)=0, wheren≥3.

scholarly journals Existence of Three Positive Solutions to Somep-Laplacian Boundary Value Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-12
Author(s):  
Moulay Rchid Sidi Ammi ◽  
Delfim F. M. Torres
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scales ◽  
Point Theorem ◽  
Boundary Value ◽  
Sufficient Conditions

We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to somep-Laplacian boundary value problems on time scales.

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