Topological Transversality: Application to an Integrodifferential Equation
Adrian Constantin · Journal of Mathematical Analysis and Applications · 1996
< < < < 2 K t , s, x F f t g s w x , t , s, x g R = R , 3 Ž . Ž . Ž . Ž . Ž . Ž . q Ž . where f , g, h g C R , R and w belongs to the class R of continuous q q Ž . nondecreasing functions on R with w r ) 0 for r ) 0 and satisfying q `Ž Ž .. H dsrw s s `. 1 Ž . Ž . Ž . Under assumptions 2 and 3 we show that 1 has a solution on Rq and we give bounds on that solution. Our discussion is based on topological transversality arguments. The last section is devoted to an application in the mathematical theory of water percolation phenomena.