We study positive solutions to the steady state reaction diffusion equation with Dirichlet boundary condition of the form: {-Δu=au-bu2-c up/1+up - K, x ∈ ω u=0, x ∈ ∂ω Here Δu = div(▽u) is the Laplacian of u, a,b,c,p,K are positive constants with p ≥ 2 and ω is a smooth bounded region with ∂ω in C2. This model describes the steady states of a logistic growth model with grazing and constant yield harvesting. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. We study the existence of positive solutions to this model. We prove our results by the method of sub-super solutions.}, references={Amann, H., Fixed point equations and nonlinear eigenvalue problems in ordered banach spaces (1976) SIAM Rev., 18, pp. 620-709; Berestycki, H., Caffarelli, L.A., Nirenberg, L., Inequalities for second-order elliptic equations with applications to unbounded domains (1996) Duke Mathematical Journal, 81 (2), pp. 467-494. , DOI 10.1215/S0012-7094-96-08117-X; Clement, Ph., Peletier, L.A., An anti-maximum principle for second order elliptic operators (1979) J. Diff. Eqns., 34 (2), pp. 218-229; Lions, P.L., On the existence of positive solutions of semilinear elliptic equations (1982) SIAM Rev., 24, pp. 441-467; May, R.M., Thresholds and breakpoints in ecosystems with a multiplicity of stable states (1977) Nature, 269, pp. 471-477; Noy-Meir, I., Stability of grazing systems an application of predator-prey graphs (1975) Journal of Ecology, 63, pp. 459-482; Oruganti, S., Shi, J., Shivaji, R., Diffusive equations with constant yield harvesting, I: Steady states (2002) Trans. Amer. Math. Soc., 354, pp. 3601-3619; Steele, J.H., Henderson, E.W., Modelling long term fluctuations in fish stocks (1984) Science, 224, pp. 985-987}, correspondence_address1={Causey, R.; Department of Mathematics and Statistics, , Mississippi State 39759, United States; email: rmc107@msstate.edu}, publisher={Belgian Mathematical Society}, issn={13701444}, language={English}, abbrev_source_title={Bull. Belg. Math. Soc. Simon Stevin}, document_type={Article}, source={Scopus},