Conservation laws with singular nonlocal sources

Several physical phenomena are modeled by conservation laws with fluxes or sources that are singular inthe origin. Here an integro-differential regularization of those problems is proposed. The existence of positive solutions with finite total variationis proved

On Very Weak Positive Solutions to Some Semilinear Elliptic Problems With Simultaneous Singular Nonlinear and Spatial Dependence Terms

We use recent results by Diaz and Rakotoson concerning very weak solutions to linear boundary value problems in order to improve previous work on existence and properties of weak positive solutions to a model example of semilinear singular elliptic problem

Semilinear elliptic equations with singular nonlinearities

We prove existence, regularity and nonexistence results for problems whose model is -Lambda u = f(x)/u gamma in Omega, with zero Dirichlet conditions on the boundary of an open, bounded subset Omega of R(N). Here gamma > 0 and f is a nonnegative function on Omega. Our results will depend on the summability of f in some Lebesgue spaces, and on the values of gamma (which can be equal, larger or smaller than 1)