Principal eigenvalue and eigenfunctions of an elliptic operator with large advection and its application to a competition model

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Approximating the ideal free distribution via reaction–diffusion–advection equations (2008, methodology): “It is also the reason why too strong a tendency to move up resource gradients without regard to crowding eects can sometimes make a population subject to invasion by another population using a dierent strategy, as in [11, 12 ].”
Effects of diffusion and advection on the principal eigenvalue of a periodic-parabolic problem with applications (2015, methodology): “To analyze the qualitative behavior of the principal eigenvalue for the elliptic operators mentioned above, the mathematical approaches developed in [5,10,11] rely heavily on the variational characterization of the principal eigenvalue.”
Reaction-diffusion-advection models for the effects and evolution of dispersal (2013, background): “For further discussion and detailed derivations of the results described above see [5, 8, 15, 16, 21, 22, 25, 40, 59, 61] and the references therein.”
Some Challenging Mathematical Problems in Evolution of Dispersal and Population Dynamics (2008, background): “Theorem 6.4. ([ 26 ]) Suppose that R m(x)dx > 0 and all critical points of”