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math.AP2023
A Probabilistic Approach to the Existence of Solutions to Semilinear Elliptic Equations
Ma Elena Hernandez-Hernandez, Pablo Padilla-Longoria
We study a semilinear elliptic equation with a pure power nonlinearity with exponent , and provide sufficient conditions for the existence of positive solutions. These conditi…
math.AP2022
Synchronization Fronts in a Spatially Extended System of Hybrid Rayleigh-van der Pol Oscillators
Carles Tardío Pi, Jorge Castillo Medina, Pablo Padilla Longoria
Numerous biological systems exhibit transitions to synchronised oscillations via a population-density-dependant mechanism known as quorum sensing. Here we propose a model system, b…