Displaying similar documents to “On a vector multipoint boundary value problem”

On the solvability of some multi-point boundary value problems

Chaitan P. Gupta, Sotiris K. Ntouyas, Panagiotis Ch. Tsamatos (1996)

Applications of Mathematics

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Let f : [ 0 , 1 ] × 2 be a function satisfying Caratheodory’s conditions and let e ( t ) L 1 [ 0 , 1 ] . Let ξ i , τ j ( 0 , 1 ) , c i , a j , all of the c i ’s, (respectively, a j ’s) having the same sign, i = 1 , 2 , ... , m - 2 , j = 1 , 2 , ... , n - 2 , 0 < ξ 1 < ξ 2 < ... < ξ m - 2 < 1 , 0 < τ 1 < τ 2 < ... < τ n - 2 < 1 be given. This paper is concerned with the problem of existence of a solution for the multi-point boundary value problems x ' ' ( t ) = f ( t , x ( t ) , x ' ( t ) ) + e ( t ) , t ( 0 , 1 ) E x ( 0 ) = i = 1 m - 2 c i x ' ( ξ i ) , x ( 1 ) = j = 1 n - 2 a j x ( τ j ) B C m n and x ' ' ( t ) = f ( t , x ( t ) , x ' ( t ) ) + e ( t ) , t ( 0 , 1 ) E x ( 0 ) = i = 1 m - 2 c i x ' ( ξ i ) , x ' ( 1 ) = j = 1 n - 2 a j x ' ( τ j ) , B C m n ' Conditions for the existence of a solution for the above boundary value problems are given using Leray-Schauder Continuation theorem.