We consider the p-Laplacian problem with the exponent of the nonlinearity p depending on the solution u. Both situations when p(u) is a local quantity or when p(u) is nonlocal are studied. 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 particular by working out the uniqueness for a one dimensional local problem and by showing that the uniqueness is easily lost in the nonlocal case. (Joint work with H.B. de Oliveira).

简介：Michel Chipot为苏黎世大学数学研究所教授，2009年当选欧洲科学院院士，Journal of Elliptic and Parabolic Equations的创始人和现任主编。

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