scholarly journals Singular boundary value problem on infinite time scale

2006 ◽  
Vol 2006 ◽  
pp. 1-13
Author(s):  
Zhao-Cai Hao ◽  
Jin Liang ◽  
Ti-Jun Xiao
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Approximation Method ◽  
Time Scale ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Infinite Time

This paper deals with a class of singular boundary value problems of differential equations on infinite time scale. An existence theorem of positive solutions is established by using the Schauder fixed point theorem and perturbation and operator approximation method, which resolves the singularity successfully and differs from those of some papers. In the end of the paper, an example is given to illustrate our main result.

Singular boundary value problems for P-Laplacian-like equations

1997 ◽  
Vol 127 (5) ◽  
pp. 975-981 ◽  
Author(s):  
D. D. Hai ◽  
Seth F. Oppenheimer
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Nonlinear Boundary Value Problems ◽  
Existence Of Positive Solutions

SynopsisWe consider the existence of positive solutions to a class of singular nonlinear boundary value problems for P-Laplacian-like equations. Our approach is based on the Schauder Fixed-Point Theorem.

EXISTENCE AND UNIQUENESS OF SOLUTIONS FOR SINGULAR BOUNDARY VALUE PROBLEM ON TIME SCALES

2012 ◽  
Vol 23 (07) ◽  
pp. 1250070 ◽  
Author(s):  
ZHENJIE LIU
Keyword(s):  
Boundary Value Problem ◽  
Time Scales ◽  
Time Scale ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Uniqueness Of Solutions ◽  
Monotone Method

This paper investigates the existence and uniqueness of solutions for singular second-order boundary value problem on time scales by using mixed monotone method. The theorems obtained are very general and complement the previous known results. When the time scale 𝕋 is chosen as ℝ or ℤ, the problem will be the corresponding continuous or discrete boundary value problem.

scholarly journals Positive solutions of impulsive time-scale boundary value problems with p-Laplacian on the half-line

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 415-433
Author(s):  
Karaca Yaslan ◽  
Aycan Sinanoglu
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Time Scale ◽  
Boundary Value ◽  
Dynamic Equations ◽  
Half Line ◽  
Existence Of Positive Solutions

In this paper, four functionals fixed point theorem is used to investigate the existence of positive solutions for second-order time-scale boundary value problem of impulsive dynamic equations on the half-line.

scholarly journals Conditions for the solvability of singular boundary value problems

1996 ◽  
Vol 53 (3) ◽  
pp. 485-497
Author(s):  
Xiyu Liu
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Uniqueness Result ◽  
Necessary And Sufficient Conditions ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Necessary And Sufficient

Consider the singular boundary value problem (r(x′))′ + f(t, x) = 0, 0 < t < 1. We give necessary and sufficient conditions for this problem to have solutions. In addition, a uniqueness result is obtained.

scholarly journals POSITIVE SOLUTIONS FOR NON-RESONANT SINGULAR BOUNDARY-VALUE PROBLEMS WITH A LINEAR TERM

2007 ◽  
Vol 50 (1) ◽  
pp. 217-228 ◽  
Author(s):  
Haishen Lü ◽  
Donal O’Regan ◽  
Ravi P. Agarwal
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Linear Term ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems

AbstractThis paper presents new existence results for the singular boundary-value problem\begin{gather*} -u''+p(t)u=f(t,u),\quad t\in(0,1),\\ u(0)=0=u(1). \end{gather*}In particular, our nonlinearity $f$ may be singular at $t=0,1$ and $u=0$.

scholarly journals On a Constructive Approach for Derivative-Dependent Singular Boundary Value Problems

2011 ◽  
Vol 2011 ◽  
pp. 1-16 ◽  
Author(s):  
R. K. Pandey ◽  
Amit K. Verma
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Of Solution ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems ◽  
Constructive Approach

We present a constructive approach to establish existence and uniqueness of solution of singular boundary value problem-(p(x)y′(x))′=q(x)f(x,y,py′)for0<x≤b,y(0)=a,α1y(b)+β1p(b)y′(b)=γ1.Herep(x)>0on(0,b)allowingp(0)=0. Furtherq(x)may be allowed to have integrable discontinuity atx=0, so the problem may be doubly singular.

scholarly journals Existence theory for nonresonant singular boundary value problems

1995 ◽  
Vol 38 (3) ◽  
pp. 431-447 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Trivial Solution ◽  
Boundary Value ◽  
Existence Results ◽  
Existence Theory ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Singular Boundary Value Problems

We present some existence results for the “nonresonant” singular boundary value problem a.e. on [0, 1] with Here μ is such that a.e. on [0, 1] with has only the trivial solution.

scholarly journals Existence of Positive Solutions for a Kind of Fractional Boundary Value Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hongjie Liu ◽  
Xiao Fu ◽  
Liangping Qi
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Fractional Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Boundary Value Problems

We are concerned with the following nonlinear three-point fractional boundary value problem:D0+αut+λatft,ut=0,0<t<1,u0=0, andu1=βuη, where1<α≤2,0<β<1,0<η<1,D0+αis the standard Riemann-Liouville fractional derivative,at>0is continuous for0≤t≤1, andf≥0is continuous on0,1×0,∞. By using Krasnoesel'skii's fixed-point theorem and the corresponding Green function, we obtain some results for the existence of positive solutions. At the end of this paper, we give an example to illustrate our main results.

scholarly journals Existence of Multiple Positive Solutions for Even Order Multi-Point Boundary Value Problems

2007 ◽  
Vol 14 (4) ◽  
pp. 775-792
Author(s):  
Youyu Wang ◽  
Weigao Ge
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Multiple Positive Solutions ◽  
Point Boundary ◽  
Even Order

Abstract In this paper, we consider the existence of multiple positive solutions for the 2𝑛th order 𝑚-point boundary value problem: where (0,1), 0 < ξ 1 < ξ 2 < ⋯ < ξ 𝑚–2 < 1. Using the Leggett–Williams fixed point theorem, we provide sufficient conditions for the existence of at least three positive solutions to the above boundary value problem. The associated Green's function for the above problem is also given.

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