The purpose of this paper is to use an appropriate variational framework to discuss the boundary value problem with p-Laplacian type operators $${({alpha}(t,x^{Delta}(t)))^{Delta}-a(t){phi}_p(x^{sigma}(t))+f({sigma}(t),x^{sigma}(t))=0,;{Delta}-a.e.;t{in}I\x^{sigma}(0)=0,\{eta}_1x^{sigma}(1)+{eta}_2x^{Delta}({sigma}(1))=0,$$ where ${eta}_1$, ${eta}_2$ > 0, $I=[0,1]^{k^2}$, ${alpha}({cdot},x({cdot}))$ is an operator of $p$-Laplacian type, $mathbb{T}$ is a time scale. Some sufficient conditions for the existence of constant-sign solutions are obtained.