Abstract
Several new existence theorems on positive, negative, and sign-changing 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, wheref∈C([0,1]×ℝ1,ℝ1). In particular, an infinitely many sign changing solution theorem is established. The method of the invariant set of decreasing flow is employed to discuss this problem.
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