Abstract
In this paper, we are concerned with the fourth-order two-point boundary value problem u ( i v ) ( t ) = f ( t , u ( t ) , u ′ ( t ) , u ″ ( t ) , u ‴ ( t ) ) , 0 < t < 1 , u ( 0 ) = u ′ ( 1 ) = u ″ ( 0 ) = u ‴ ( 1 ) = 0 . By placing certain restrictions on the nonlinear term f , we obtain the existence results for the fourth-order two-point boundary value problem via the lower and upper solution method. In particular, a new truncating technique and an appropriate Nagumo-type condition are introduced and employed.
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