DOI10.1017/S030821050001876XzbMath0711.92020OpenAlexW2126716506MaRDI QIDQ3496198
Robert Stephen Cantrell, Chris Cosner
Publication date: 1989
Published in: Proceedings of the Royal Society of Edinburgh: Section A Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1017/s030821050001876x
Steiner symmetry in the minimization of the first eigenvalue of a fractional eigenvalue problem with indefinite weight ⋮
Quantitative Stability for Eigenvalues of Schrödinger Operator, Quantitative Bathtub Principle, and Application to the Turnpike Property for a Bilinear Optimal Control Problem ⋮
Impact of resource distributions on the competition of species in stream environment ⋮
Multiple positive steady states of a diffusive predator‐prey model in spatially heterogeneous environments ⋮
Adaptation in a heterogeneous environment. II: To be three or not to be ⋮
Inverse power method for the principal eigenvalue of the Robin \(p\)-Laplacian ⋮
Dynamics of a periodic-parabolic Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮
Spectral optimization for weighted anisotropic problems with Robin conditions ⋮
On the optimization of the first weighted eigenvalue ⋮
Coexistence-segregation dichotomy in the full cross-diffusion limit of the stationary SKT model ⋮
On the logistic equation for the fractional p‐Laplacian ⋮
Enhancing population persistence by a protection zone in a reaction-diffusion model with strong Allee effect ⋮
A mathematical study of diffusive logistic equations with mixed type boundary conditions ⋮
Singular Analysis of the Optimizers of the Principal Eigenvalue in Indefinite Weighted Neumann Problems ⋮
A single consumer model with Neumann boundary condition ⋮
\( L^2 \)-gradient flows of spectral functionals ⋮
Maximizing Metapopulation Growth Rate and Biomass in Stream Networks ⋮
A basic theory for initial value problems of first order ordinary differential equations with \(L^p\)-Carathéodory functions and applications ⋮
Quantitative Analysis of a Singularly Perturbed Shape Optimization Problem in a Polygon ⋮
Limiting profile for stationary solutions maximizing the total population of a diffusive logistic equation ⋮
On the dynamics of predator-prey models with the Beddington-DeAngelis functional response ⋮
OPTIMAL RESOURCE ALLOCATION FOR A DIFFUSIVE POPULATION MODEL ⋮
Bifurcation and stability of solutions to a logistic equation with harvesting ⋮
Optimal location of resources and Steiner symmetry in a population dynamics model in heterogeneous environments ⋮
On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications ⋮
Global stability in models of population dynamics with diffusion. II: Continuously varying environments ⋮
Allee effect and bistability in a spatially heterogeneous predator-prey model ⋮
The singular perturbation problem for the periodic-parabolic logistic equation with indefinite weight functions ⋮
Positive solutions of Neumann boundary value problems and applications to logistic type population models ⋮
Lie point symmetries, conservation laws, and solutions of a space dependent reaction-diffusion equation ⋮
Positive steady states of reaction-diffusion-advection competition models in periodic environment ⋮
Diffusive logistic equation with constant yield harvesting, I: Steady States ⋮
Spots, traps, and patches: asymptotic analysis of localized solutions to some linear and nonlinear diffusive systems ⋮
Lyapunov type inequalities for Hammerstein integral equations and applications to population dynamics ⋮
Permanence in ecological systems with spatial heterogeneity ⋮
On the definition and the properties of the principal eigenvalue of some nonlocal operators ⋮
Modeling biological invasions into periodically fragmented environments ⋮
Maximization of the total population in a reaction-diffusion model with logistic growth ⋮
Minimization of the principal eigenvalue for an elliptic boundary value problem with indefinite weight, and applications to population dynamics ⋮
Optimal control of growth coefficient on a steady-state population model ⋮
Variability, vagueness and comparison methods for ecological models ⋮
Ecological models, permanence and spatial heterogeneity ⋮
Asymptotic properties of an optimal principal eigenvalue with spherical weight and Dirichlet boundary conditions ⋮
Steady-state analysis in a model for population diffusion in a multi-patch environment ⋮
Population diffusion in a two-patch environment ⋮
The diffusive logistic equation on periodically evolving domains ⋮
Reaction-diffusion-advection models for the effects and evolution of dispersal ⋮
Augmented coupling interface method for solving eigenvalue problems with sign-changed coefficients ⋮
Positive solutions of elliptic boundary value problems and applications to population dynamics ⋮
Existence and uniqueness of solution of the differential equation describing the TASEP-LK coupled transport process ⋮
Invasion dynamics of a predator-prey system in closed advective environments ⋮
Global structure of supercritical bifurcation with turning points for the logistic elliptic equation with nonlinear boundary conditions ⋮
Uniqueness and stability of positive steady state solutions for a ratio-dependent predator-prey system with a crowding term in the prey equation ⋮
Gradient estimates for a nonlinear parabolic equation and Liouville theorems ⋮
Existence and the dynamical behaviors of the positive solutions for a ratio-dependent predator-prey system with the crowing term and the weak growth ⋮
Uniqueness and stability of positive solutions for a diffusive predator-prey model in heterogeneous environment ⋮
Analyticity of free boundary in an optimal harvesting problem ⋮
Stochastic population growth in spatially heterogeneous environments ⋮
Optimal harvesting strategy based on rearrangements of functions ⋮
A diffusive logistic equation with a free boundary and sign-changing coefficient in time-periodic environment ⋮
Global stability in models of population dynamics with diffusion. I. Patchy environments ⋮
Global dynamics of a general Lotka-Volterra competition-diffusion system in heterogeneous environments ⋮
The bang-bang property in some parabolic bilinear optimal control problems \textit{via} two-scale asymptotic expansions ⋮
A revisit to the diffusive logistic model with free boundary condition ⋮
Principal eigenvalue minimization for an elliptic problem with indefinite weight and Robin boundary conditions ⋮
Study of a Mixed Dispersal Population Dynamics Model ⋮
Diffusion-mediated permanence problem for a heterogeneous Lotka–Volterra competition model ⋮
On the ratio of total masses of species to resources for a logistic equation with Dirichlet boundary condition ⋮
The diffusive logistic model with a free boundary in heterogeneous environment ⋮
Practical persistence in ecological models via comparison methods ⋮
Optimization of species survival for logistic models with non-local dispersal ⋮
Global attractivity and stability in some monotone discrete dynamical systems ⋮
Positive maximal and minimal solutions for non-homogeneous elliptic equations depending on the gradient ⋮
The spreading front of invasive species in favorable habitat or unfavorable habitat ⋮
Conservation laws and exact solutions for a reaction-diffusion equation with a variable coefficient ⋮
Nonlocal refuge model with a partial control ⋮
Species persistence decreases with habitat fragmentation: an analysis in periodic stochastic environments ⋮
Reaction-diffusion equations in space-time periodic media ⋮
Best dispersal strategies in spatially heterogeneous environments: optimization of the principal eigenvalue for indefinite fractional Neumann problems ⋮
On generalized principal eigenvalues of nonlocal operators with a drift ⋮
A nonlocal diffusion model with free boundaries in spatial heterogeneous environment ⋮
Newtonian potential and positive solutions of Poisson equations ⋮
The behaviour, of stationary solutions to some nonlinear diffusion problems ⋮
Properties of optimizers of the principal eigenvalue with indefinite weight and Robin conditions ⋮
Mathematical analysis of the optimal habitat configurations for species persistence ⋮
Hopf bifurcation in a delayed reaction-diffusion-advection population model ⋮
Local dynamics of a diffusive predator-prey model in spatially heterogeneous environment ⋮
Effect of harvesting quota and protection zone in a reaction-diffusion model arising from fishery management ⋮
Spectral theory for nonlocal dispersal operators with time periodic indefinite weight functions and applications ⋮
The diffusive logistic equation with a free boundary and sign-changing coefficient ⋮
Optimization of the First Eigenvalue of Equations with Indefinite Weights ⋮
On the uniqueness of the positive steady state for Lotka-Volterra models with diffusion ⋮
Analysis of the periodically fragmented environment model. I: Species persistence ⋮
Spectrum and constant sign solutions for a fractional Laplace problem with sign-changing weight ⋮
Blowing-up properties of the positive principal eigenvalue for indefinite Robin-type boundary conditions ⋮
An indefinite concave-convex equation under a Neumann boundary condition. I ⋮
Numerical simulation for a nonlinear partial differential equation with variable coefficients by means of the discrete variational derivative method ⋮
EFFECTS OF DOMAIN SIZE ON THE PERSISTENCE OF POPULATIONS IN A DIFFUSIVE FOOD-CHAIN MODEL WITH BEDDINGTON-DeANGELIS FUNCTIONAL RESPONSE ⋮
Persistence in reaction diffusion models with weak Allee effect ⋮
Existence and uniqueness of the solution of a space-time periodic reaction-diffusion equation
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