scholarly journals Positive solutions for higher-order Lidstone boundary value problems. A new approach via Sperner's Lemma

2001 ◽  
Vol 42 (1-2) ◽  
pp. 75-89 ◽  
Author(s):  
P.K. Palamides
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Boundary Value ◽  
Higher Order ◽  
New Approach ◽  
Sperner’S Lemma

Higher-order singular multi-point boundary-value problems on time scales

2011 ◽  
Vol 54 (2) ◽  
pp. 345-361 ◽  
Author(s):  
Abdulkadir Dogan ◽  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Boundary Value Problems ◽  
Positive Solutions ◽  
Operator Theory ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Higher Order ◽  
Singular Boundary ◽  
Singular Boundary Value Problems ◽  
Mixed Monotone Operator ◽  
Monotone Operator Theory

AbstractWe study classes of higher-order singular boundary-value problems on a time scale $\mathbb{T}$ with a positive parameter λ in the differential equations. A homeomorphism and homomorphism ø are involved both in the differential equation and in the boundary conditions. Criteria are obtained for the existence and uniqueness of positive solutions. The dependence of positive solutions on the parameter λ is studied. Applications of our results to special problems are also discussed. Our analysis mainly relies on the mixed monotone operator theory. The results here are new, even in the cases of second-order differential and difference equations.

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