Enguiça, Ricardo RoqueGavioli, AndreaSanchez, Luis2014-09-162014-09-162013-01ENGUIÇA, Ricardo; GAVIOLI, Andrea; SANCHEZ, Luis - A class of singular first order differential equations with applications in reaction-diffusion. Discrete and Continuous Dynamical Systems. Vol. 33, nr. 1 (2013), p. 173-191.1078-0947http://hdl.handle.net/10400.21/3812Agências Financiadoras: FCT e MIURWe study positive solutions y(u) for the first order differential equation y' = q(cy(1/p) - f(u)) where c > 0 is a parameter, p > 1 and q > 1 are conjugate numbers and f is a continuous function in [0, 1] such that f(0) = 0 = f(1). We shall be particularly concerned with positive solutions y(u) such that y(0) = 0 = y(1). Our motivation lies in the fact that this problem provides a model for the existence of travelling wave solutions for analogues of the FKPP equation in one space dimension, where diffusion is represented by the p-Laplacian operator. We obtain a theory of admissible velocities and some other features that generalize classical and recent results, established for p = 2.engp-LaplacianFKPP equationHeteroclinicTravelling waveCritical speedSharp solutionjournal article10.3934/dcds.2013.33.173