We study the existence and multiplicity of positive solutions of the following boundary-value problem: -u(6)-γu(4)+βu′′-αu=f(t,u), 0<t<1, u(0)=u(1)=u′′(0)=u′′(1)=u(4)(0)=u(4)(1)=0, where f:[0,1]×R⁺ → R⁺ is continuous, α, β, and γ∈R satisfy some suitable assumptions.