Existence of infinitely many solutions of a beam equation with non-monotone nonlinearity

In this paper, we prove a new critical point theorem without the (PS)∗ condition or the (WPS)∗ condition. Using this theorem, we prove the existence of infinitely many solutions of the following sublinear beam equation {utt+uxxxx+f(x,t,u)=0for(x,t)∈Q=(0,π)×(0,2π)u(0,t)=u(π,t)=uxx(0,t)=uxx(π,t)fort∈Ru(x,t)=u(t+2π,x)fort∈(0,π)×R. Unlike the previous results on this equation, we do not impose any monotone conditions on the variable ξξ in the nonlinearity f(x,t,ξ)f(x,t,ξ).