Existence and Uniqueness Theorems for Three–Point Boundary Value Problems

1989 ◽  
Vol 20 (3) ◽  
pp. 716-726 ◽  
Author(s):  
A. R. Aftabizadeh ◽  
Chaitan P. Gupta ◽  
Jian-Ming Xu
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Point Boundary ◽  
Existence And Uniqueness Theorems

Monotone techniques and some existence-uniqueness theorems for two point boundary value problems

1982 ◽  
Vol 91 (3-4) ◽  
pp. 265-275
Author(s):  
Song-Sun Lin
Keyword(s):  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Boundary Value ◽  
Uniqueness Theorems ◽  
Point Boundary ◽  
Equivalent Problem ◽  
Least Eigenvalue ◽  
Optimal Bounds ◽  
Linear Problems ◽  
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SynopsisIn this paper we study the existence and uniqueness of the two point boundary value problems −(p(x)u′(x))′ = f(x, u(x), u′(x)), xε(0, 1), u′(0)−cu(0) = 0 = u′(1) + du(1), where ∂f/∂u is bounded. above by the least eigenvalue of associated linear problems and ∂f/∂u is bounded. By using monotone techniques to investigate the equivalent problem −(p(x)u′(x))′ + r(x)u(x) = f(x, u(x), u′(x)) + r(x)u(x) where r ε C[0, 1] we show thatgives the optimal bounds for ∂f/∂u and ∂f/u′ when c and d are nonnegative constants.

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