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 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 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 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.

Solvability of Some Singular Boundary Value Problems on the Semi-Infinite Interval

1996 ◽  
Vol 48 (1) ◽  
pp. 143-158 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Existence Results ◽  
Nonlinear Boundary Value Problem ◽  
Infinite Interval ◽  
Singular Boundary ◽  
Singular Boundary Value Problems

AbstractExistence of solutions to the nonlinear boundary value problem on the semi-infinite interval bounded on [0, ∞), are established. In the process we obtain new existence results for boundary value problems on compact intervals.

scholarly journals EXISTENCE OF POSITIVE SOLUTIONS FOR BOUNDARY-VALUE PROBLEMS WITH SINGULARITIES IN PHASE VARIABLES

2004 ◽  
Vol 47 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ravi P. Agarwal ◽  
Donal O’Regan ◽  
Svatoslav Staněk
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Positive Solution ◽  
Positive Solutions ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Existence Of Positive Solutions ◽  
Carathéodory Conditions ◽  
Primary 34B16

AbstractThe singular boundary-value problem $(g(x'))'=\mu f(t,x,x')$, $x'(0)=0$, $x(T)=b>0$ is considered. Here $\mu$ is the parameter and $f(t,x,y)$, which satisfies local Carathéodory conditions on $[0,T]\times(\mathbb{R}\setminus\{b\})\times(\mathbb{R}\setminus\{0\})$, may be singular at the values $x=b$ and $y=0$ of the phase variables $x$ and $y$, respectively. Conditions guaranteeing the existence of a positive solution to the above problem for suitable positive values of $\mu$ are given. The proofs are based on regularization and sequential techniques and use the topological transversality theorem.AMS 2000 Mathematics subject classification: Primary 34B16; 34B18

scholarly journals Existence Results for Singular Boundary Value Problem of Nonlinear Fractional Differential Equation

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
Yujun Cui
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value ◽  
Existence Results ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Fractional Boundary Value Problem ◽  
Nonlinear Fractional Differential Equation ◽  
Existence Of Positive Solutions ◽  
Liouville Fractional Derivative ◽  
Fractional Differential

By applying a fixed point theorem for mappings that are decreasing with respect to a cone, this paper investigates the existence of positive solutions for the nonlinear fractional boundary value problem: , , , where , is the Riemann-Liouville fractional derivative.

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.

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