The Solutions for Semi-Positone Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

2011 ◽  
pp. 539-542
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Linear Functional ◽  
Boundary Value ◽  
Half Line ◽  
Functional Boundary ◽  
Functional Boundary Conditions

scholarly journals Existence of2m-1Positive Solutions for Sturm-Liouville Boundary Value Problems with Linear Functional Boundary Conditions on the Half-Line

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
Yanmei Sun ◽  
Zengqin Zhao
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Linear Functional ◽  
Boundary Value ◽  
Half Line ◽  
Multiple Positive Solutions ◽  
Functional Boundary ◽  
Sturm Liouville ◽  
Functional Boundary Conditions

By using the Leggett-Williams fixed theorem, we establish the existence of multiple positive solutions for second-order nonhomogeneous Sturm-Liouville boundary value problems with linear functional boundary conditions. One explicit example with singularity is presented to demonstrate the application of our main results.

scholarly journals Existence of solutions for functional boundary value problems at resonance on the half-line

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Bingzhi Sun ◽  
Weihua Jiang
Keyword(s):  
Boundary Value Problems ◽  
Banach Spaces ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Coincidence Degree ◽  
Degree Theory ◽  
Half Line ◽  
Projection Scheme ◽  
At Resonance ◽  
Functional Boundary

Abstract By defining the Banach spaces endowed with the appropriate norm, constructing a suitable projection scheme, and using the coincidence degree theory due to Mawhin, we study the existence of solutions for functional boundary value problems at resonance on the half-line with $\operatorname{dim}\operatorname{Ker}L = 1$ dim Ker L = 1 . And an example is given to show that our result here is valid.

Uniqueness of positive solutions of some semilinear Sturm–Liouville problems on the half line

1984 ◽  
Vol 97 ◽  
pp. 259-263 ◽  
Author(s):  
J. F. Toland
Keyword(s):  
Boundary Conditions ◽  
Boundary Value Problems ◽  
Positive Solutions ◽  
Simple Proof ◽  
Boundary Value ◽  
Half Line ◽  
Linear Boundary ◽  
Autonomous Case ◽  
Sturm Liouville ◽  
Image Position

SynopsisThis note gives a simple proof of uniqueness for positive solutions of certain non-linear boundary value problems on ℝ+ which are typified by the equationwith boundary conditions u′(0) = u(+∞) = 0. In the autonomous case (r ≡ 1), this is easy to see, by quadrature. The proof here supposes r to be non-increasing on ℝ+.

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