scholarly journals INVARIANT IMBEDDING AND THE REDUCTION OF TWO-POINT BOUNDARY VALUE PROBLEMS TO INITIAL VALUE PROBLEMS

1960 ◽  
Vol 46 (12) ◽  
pp. 1646-1649 ◽  
Author(s):  
R. Bellman ◽  
R. Kalaba ◽  
G. M. Wing
Keyword(s):  
Boundary Value Problems ◽  
Initial Value Problems ◽  
Boundary Value ◽  
Point Boundary ◽  
Invariant Imbedding ◽  
Initial Value

Existence and uniqueness for two-point boundary value problems

1981 ◽  
Vol 88 (3-4) ◽  
pp. 219-234 ◽  
Author(s):  
John V. Baxley ◽  
Sarah E. Brown
Keyword(s):  
Boundary Value Problem ◽  
Boundary Value Problems ◽  
Existence And Uniqueness ◽  
Initial Value Problems ◽  
Shooting Method ◽  
Nonlinear Boundary ◽  
Boundary Value ◽  
Nonlinear Boundary Conditions ◽  
Point Boundary ◽  
Initial Value

SynopsisBoundary value problems associated with y″ = f(x, y, y′) for 0 ≦ x ≦ 1 are considered. Using techniques based on the shooting method, conditions are given on f(x, y,y′) which guarantee the existence on [0, 1] of solutions of some initial value problems. Working within the class of such solutions, conditions are then given on nonlinear boundary conditions of the form g(y(0), y′(0)) = 0, h(y(0), y′(0), y(1), y′(1)) = 0 which guarantee the existence of a unique solution of the resulting boundary value problem.

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