Sign-changing and multiple solutions of the Sturm–Liouville boundary value problem via invariant sets of descending flow

In this paper, we prove the existence of sign-changing and multiple solutions for the second-order Sturm–Liouville boundary value problem {−Lu=f(x,u),x∈[0,1]R1(u)=0,R2(u)=0, where Lu=(p(x)u′)′−q(x)uLu=(p(x)u′)′−q(x)u is the Sturm–Liouville operator, R1(u)=αu′(0)−βu(0)R1(u)=αu′(0)−βu(0) and R2(u)=γu′(1)+σu(1)R2(u)=γu′(1)+σu(1). The technical approach is fully based on minimax methods and invariant sets of descending flow.