We study the nonlocal nonlinear problem (-Δ)su=λf(u)inΩ,u=0onRN\\Ω,(Pλ)\\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}$$\\begin{aligned} \\left\\{ \\begin{array}[c]{lll} (-\\Delta )^s u = \\lambda f(u) &{} \\text{ in } \\Omega , \\\\ u=0&{}\\text{ on } \\mathbb {R}^N{\\setminus }\\Omega , \\quad (P_{\\lambda }) \\end{array} \\right. \\end{aligned}$$\\end{document}where Omega is a bounded smooth domain in mathbb {R}^N, N>2s, 0<s<1; f:mathbb {R}rightarrow [0,infty ) is a nonlinear continuous function such that f(0)=f(1)=0 and f(t)sim |t|^{p-1}t as trightarrow 0^+, with 2<p+1<2^*_s; and lambda is a positive parameter. We prove the existence of two nontrivial solutions u_{lambda } and v_{lambda } to (P_{lambda }) such that 0le u_{lambda }< v_{lambda }le 1 for all sufficiently large lambda . The first solution u_{lambda } is obtained by applying the Mountain Pass Theorem, whereas the second, v_{lambda }, via the sub- and super-solution method. We point out that our results hold regardless of the behavior of the nonlinearity f at infinity. In addition, we obtain that these solutions belong to L^{infty }(Omega ).