Existence and uniqueness theorems for fourth-order boundary value problems

y(0) =A1, y(1)=A2, y"(0) -B1, y"(1) = B2. In this paper we shall consider a more general problem, namely, y(4) = f ( x , y, y") (1.1) whe re fe C[ [-0, 1 ] x R x R, R], under the following types of boundary conditions: y(0) =yo, y ( 1 ) = y i , y"(0) =)7o, y"(1) =371 ; (1.2) y(0) =yo, y ( 1 ) = y l , y"(0) = )7o, y " ( 1 ) = y l ; (1.3) y(0) = y(1 ) = y"(0) = y"(1 ) = 0; (1.4) y(0) =y(1) = 0, y" ' (O)-hy"(O)=O, y " ( 1 ) + k y " ( 1 ) = O , (1.5)