W. Allegretto and P.O. Odiobala, Nonpositone elliptic problems in RN , Proc. Amer. Math. Soc. 123 (1995), no.] 2, 533–541.

S. Carl, D. Costa and H.T. Tehrani, D1,2 (RN ) versus C(RN ) local minimizer and a Hopf-type maximum principle, J. Differential Equations 261 (2016), no. 3, 2006–2025.

S. Carl, D. Costa and H.T. Tehrani, D1,2 (RN ) versus C(RN ) local minimizer on manifolds and multiple solutions for zero mass equations in RN , Adv. Calc. Var. 11 (2018), no. 3, 257–272.

Ph. Clément and L.A. Peletier, An anti-maximum principle for second-order elliptic operators, J. Differential Equations 34 (1979), no. 2, 218–229.

D.G. Costa, P. Drábek and H.T. Tehrani, Positive solutions to semilinear elliptic equations with logistic type nonlinearities and constant yield harvesting in RN , Comm. Partial Differential Equations 33 (2008), no. 7–9, 1597–1610.

E.N. Dancer, On the indices of fixed points of mappings in cones and applications, J. Math. Anal. Appl. 91 (1983), no. 1, 131–151.

D.G. de Figueiredo and J.-P. Gossez, Strict monotonicity of eigenvalues and unique continuation, Comm. Partial Differentail Equations 17 (1992), no. 1–2, 339–346.

Y. Du and Q. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Math. Anal. 31 (1999), no. 1, 1–18.

Y. Du and L. Ma, Positive solutions of an elliptic partial differential equation on RN , J. Math. Anal. Appl. 271 (2002), no. 2, 409–425.

Y. Du and Li Ma, Logistic type equations on RN by a squeezing method involving boundary blow-up solutions, J. London Math. Soc. (2) 64 (2001), no. 1, 107–124.

Y. Du and J. Shi, Allee effect and bistability in a spatially heterogeneous predator-prey model, Trans. Amer. Math. Soc. 359 (2007), no. 9, 4557–4593.

D. Gilbarg and N.S. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer–Verlag, Berlin, 2001, reprint of the 1998 edition.

P. Girão and H. Tehrani, Positive solutions to logistic type equations with harvesting, J. Differential Equations 247 (2009), no. 2, 574–595.

P.M. Girão, Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue, Nonlinear Anal. 74 (2011), no. 1, 94–113.

P.M. Girão and M. Pérez-Llanos, Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction, J. Math. Anal. Appl. 403 (2013), no. 2, 376–390.

S. Oruganti and J. Shi and R. Shivaji, Diffusive logistic equation with constant yield harvesting I. Steady states, Trans. Amer. Math. Soc. 354 (2002), no. 9, 3601–3619 (electronic).

T. Ouyang, On the positive solutions of semilinear equations ∆u + λu − hup = 0 on the compact manifolds, Trans. Amer. Math. Soc. 331 (1992), no. 2, 503–527.

D.H. Sattinger, Monotone methods in nonlinear elliptic and parabolic boundary value problems, Indiana Univ. Math. J. 21 (1971/72), 979–1000.

S. Shabani, Diffusive Holling type-II predator-prey system with harvesting of prey, J. Math. Anal. Appl. 410 (2014), no. 1, 469–482.

S. Shabani Rokn-e-vafa and H.T. Tehrani, Diffusive logistic equations with harvesting and heterogeneity under strong growth rate, Adv. Nonlinear Anal. 8 (2019), no. 1, 455–467.

M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, fourth edition, Springer–Verlag, Berlin, 2008.