Infinitely Many Sign-Changing Solutions for Some Nonlinear Fourth-Order Beam Equations

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, where f∈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.