Chipot, M.de Oliveira, H. B.2020-07-242020-07-242019-100025-58311432-1807http://hdl.handle.net/10400.1/14242The p-Laplacian problem with the exponent of nonlinearity p depending on the solution u itself is considered in this work. Both situations when p(u) is a local quantity or when p(u) is nonlocal are studied here. For the associated boundary-value local problem, we prove the existence of weak solutions by using a singular perturbation technique. We also prove the existence of weak solutions to the nonlocal version of the associated boundary-value problem. The issue of uniqueness for these problems is addressed in this work as well, in particular by working out the uniqueness for a one dimensional local problem and by showing that the uniqueness is easily lost in the nonlocal problem.engjournal article10.1007/s00208-019-01803-w