Existence of Positive Solutions for a Singular Boundary Value Problem on the Half-line

2012 ◽  
Vol 14 (3) ◽  
pp. 225
Author(s):  
Bianxia YANG ◽  
Ruipeng CHEN
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Half Line ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Existence Of Positive Solutions

scholarly journals Positive Solutions of Nonresonant Singular Boundary Value Problem of Second Order Differential Equations

2001 ◽  
Vol 162 ◽  
pp. 127-148 ◽  
Author(s):  
Zhongli Wei ◽  
Changci Pang
Keyword(s):  
Differential Equations ◽  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Second Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Second Order Differential Equations ◽  
Existence Of Positive Solutions ◽  
Necessary And Sufficient

This paper investigates the existence of positive solutions of nonresonant singular boundary value problem of second order differential equations. A necessary and sufficient condition for the existence of C[0, 1] positive solutions as well as C1[0, 1] positive solutions is given by means of the method of lower and upper solutions with the fixed point theorems.

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

Existence of positive solutions to a higher order singular boundary value problem with fractional q-derivatives

2013 ◽  
Vol 16 (3) ◽  
Author(s):  
John Graef ◽  
Lingju Kong
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Sufficient Conditions ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Liouville Type ◽  
Nonlinear Alternative ◽  
Existence Of Positive Solutions

AbstractThe authors study the singular boundary value problem with fractional q-derivatives $\begin{gathered} - (D_q^\nu u)(t) = f(t,u),t \in (0,1), \hfill \\ (D_q^i u)(0) = 0,i = 0,...,n - 2,(D_q u)(1) = \sum\limits_{j = 1}^m {a_j (D_q u)(t_j ) + \lambda ,} \hfill \\ \end{gathered} $, where q ∈ (0, 1), m ≥ 1 and n ≥ 2 are integers, n − 1 < ν ≤ n, λ ≥ 0 is a parameter, f: (0, 1] × (0,∞) → [0,∞) is continuous, a i ≥ 0 and t i ∈ (0, 1) for i = 1, …,m, and D qν is the q-derivative of Riemann-Liouville type of order ν. Sufficient conditions are obtained for the existence of positive solutions. Their analysis is mainly based on a nonlinear alternative of Leray-Schauder.

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