General existence principles for nonlocal boundary value problems with 耳 -laplacian and their applications

作者：Ravi P Agarwal; Donal O' Regan; Svatoslav Stank

来源：Abstract and Applied Analysis, 2006.

The paper presents general existence principles which can be used for a large class of nonlocal boundary value problems of the form ( 耳 ( x ∩ ) ) ∩ = f 1 ( t , x , x ∩ ) + f 2 ( t , x , x ∩ ) F 1 x + f 3 ( t , x , x ∩ ) F 2 x , 汐 ( x ) = 0 , 汕 ( x ) = 0 , where f j satisfy local Carath谷odory conditions on some [ 0 , T ] ℅ j 2 , f j are either regular or have singularities in their phase variables ( j = 1 , 2 , 3 ) , F i : C 1 [ 0 , T ] ↙ C 0 [ 0 , T ] ( i = 1 , 2 ) , and 汐 , 汕 : C 1 [ 0 , T ] ↙ are continuous. The proofs are based on the Leray-Schauder degree theory and use regularization and sequential techniques. Applications of general existence principles to singular BVPs are given.