Abstract
Several new existence theorems on three solutions and infinitely many solutions for the following fourth-order beam equation are obtained: u ( 4 ) = f ( t , u ( t ) ) , t ∈ [ 0 , 1 ] ; u ( 0 ) = u ( 1 ) = u ″ ( 0 ) = u ″ ( 1 ) = 0 , where f ∈ C 1 ( [ 0 , 1 ] × R 1 , R 1 ) . The Morse theory is employed to discuss this problem.
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