We consider some reaction-diffusion equations describing systems with the nonlocal consumption of resources and the intraspecific competition. Sharp conditions on the coefficients are obtained to ensure the stability and instability of nontrivial constant stationary solutions.
Stability and instability of Kelvin waves
Homogenization of a class of integro-differential equations with L{é}vy operators
Stability, instability, and blowup for time fractional and other non-local in time semilinear subdiffusion equations
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