scholarly journals Positive Solutions for a Third-Order Three-Point Singular Boundary Value Problem

2016 ◽  
Vol 05 (01) ◽  
pp. 24-30
Author(s):  
红萍 吴
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Third Order

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.

On a singular nonlinear semilinear elliptic problem

1998 ◽  
Vol 128 (6) ◽  
pp. 1389-1401 ◽  
Author(s):  
Junping Shi ◽  
Miaoxin Yao
Keyword(s):  
Boundary Value Problem ◽  
Positive Solutions ◽  
Elliptic Problem ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Semilinear Elliptic Problem ◽  
Semilinear Elliptic ◽  
Image Position

We consider the singular boundary value problemWe study the existence, uniqueness, regularity and the dependency on parameters of the positive solutions under various assumptions.

On a Three-Point Boundary Value Problem for Third Order Differential Equations with Singularities in Phase Variables

2007 ◽  
Vol 14 (2) ◽  
pp. 361-383
Author(s):  
Svatoslav Staněk
Keyword(s):  
Boundary Value Problem ◽  
Convergence Theorem ◽  
Boundary Value ◽  
Singular Boundary ◽  
Singular Boundary Value Problem ◽  
Point Boundary ◽  
Third Order ◽  
Fatou Theorem ◽  
Carathéodory Conditions ◽  
Dominated Convergence

Abstract The singular boundary value problem (ϕ(𝑥″))′ = 𝑓(𝑡, 𝑥, 𝑥′, 𝑥″), 𝑥(0) = 𝑥(𝑇1) = 𝑥(𝑇) = 0 is considered. Here 0 < 𝑇1 < 𝑇, ϕ is an increasing homeomorphism from ℝ onto ℝ, positive 𝑓 satisfies the local Carathéodory conditions on [0, 𝑇] × (ℝ \ {0})3 and 𝑓 may be singular at the value 0 of all its phase variables. The conditions guaranteeing the solvability of the above problem are presented. The proofs are based on regularization and sequential techniques and in limit processes a combination of the Fatou theorem and the Lebesgue dominated convergence theorem is used.

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