A key issue in ecology is whether a population will survive long term or go extinct. This is the question we address in this paper for a population in a bounded habitat. We will restrict our study to the case of a single species in a one-dimensional habitat of length L. The evolution of the population density distribution ρ(x, t), where x is the position and t the time, is governed by elementary processes such as growth and dispersal, which, in standard models, are typically described by a constant per capita growth rate and normal diffusion, respectively. However, feedbacks in the regulatory mechanisms and external factors can produce density-dependent rates. Therefore, we consider a generalization of the standard evolution equation, which, after dimensional scaling and assuming large carrying capacity, becomes ∂ t ρ = ∂ x ( ρ ν − 1 ∂ x ρ ) + ρ μ , where μ , ν ∈ R . This equation is complemented by absorbing boundaries, mimicking adverse conditions outside the habitat. For this nonlinear problem, we obtain, analytically, exact expressions of the critical habitat size L c for population survival, as a function of the exponents and initial conditions. We find that depending on the values of the exponents (ν, μ), population survival can occur for either L ≥ L c , L ≤ L c or for any L. This generalizes the usual statement that L c represents the minimum habitat size. In addition, nonlinearities introduce dependence on the initial conditions, affecting L c .