Multiple solutions of some nonlinear fourth-order beam equations

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∈C1([0,1]×R1,R1)f∈C1([0,1]×R1,R1). The Morse theory is employed to discuss this problem.