The aim of this paper is to consider a fully cantilever beam equation with one end fixed and the other connected to a resilient supporting device, that is, \t\t\t{u(4)(t)=f(t,u(t),u′(t),u″(t),u‴(t)),t∈[0,1],u(0)=u′(0)=0,u″(1)=0,u‴(1)=g(u(1)),\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$ \\textstyle\\begin{cases} u^{(4)}(t)=f(t,u(t),u'(t),u''(t),u'''(t)), \\quad t\\in [0,1], \\\\ u(0)=u'(0)=0, \\\\ u''(1)=0,\\qquad u'''(1)=g(u(1)), \\end{cases} $$\\end{document} where f:[0,1]times mathbb{R}^{4}rightarrow mathbb{R}, g: mathbb{R}rightarrow mathbb{R} are continuous functions. Under the assumption of monotonicity, two existence results for solutions are acquired with the monotone iterative technique and the auxiliary truncated function method.