Shivaji, Diffusive logistic equation with constant yield harvesting I. Pérez-Llanos, Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction, J. Girão, Bifurcation curves of a logistic equation when the linear growth rate crosses a second eigenvalue, Nonlinear Anal. ![]() Tehrani, Positive solutions to logistic type equations with harvesting, J. Trudinger, Elliptic partial differential equations of second order, Classics in Mathematics, Springer–Verlag, Berlin, 2001, reprint of the 1998 edition. Shi, Allee effect and bistability in a spatially heterogeneous predator-prey model, Trans. Du and Li Ma, Logistic type equations on RN by a squeezing method involving boundary blow-up solutions, J. Ma, Positive solutions of an elliptic partial differential equation on RN, J. Huang, Blow-up solutions for a class of semilinear elliptic and parabolic equations, SIAM J. Partial Differentail Equations 17 (1992), no. Gossez, Strict monotonicity of eigenvalues and unique continuation, Comm. Dancer, On the indices of fixed points of mappings in cones and applications, J. Partial Differential Equations 33 (2008), no. Tehrani, Positive solutions to semilinear elliptic equations with logistic type nonlinearities and constant yield harvesting in RN, Comm. Peletier, An anti-maximum principle for second-order elliptic operators, J. Tehrani, D1,2 (RN ) versus C(RN ) local minimizer on manifolds and multiple solutions for zero mass equations in RN, Adv. Tehrani, D1,2 (RN ) versus C(RN ) local minimizer and a Hopf-type maximum principle, J. Odiobala, Nonpositone elliptic problems in RN, Proc. In addition we prove a new result on the positive solution set of this equation in the weak growth rate case complimenting existing results in the literature. ![]() \Delta u =\lambda a(x) u -b(x) u^2 - c h(x), \quad\text_0$ then our equation has a unique positive solution for all $c$ large, provided that $\lambda$ is in a right neighborhood of $\lambda_1 (\Omega_0)$. We study existence of positive solutions of the following heterogeneous diffusive logistic equation with a harvesting term, Diffusive logistic equation, harvesting term, strong growth rate, whole space $\mathbb R^N$ Abstract
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