Degenerate elliptic equations with measure data and nonlinear potentials
Dirichlet problem. Characterization of regularity.
Discontinuous elliptic problems in without monotonicity assumptions
We prove existence of a positive, radial solution for a semilinear elliptic problem with a discontinuous nonlinearity. We use an approximating argument which requires no monotonicity assumptions on the nonlinearity.
Discontinuous quasilinear elliptic problems at resonance
In this paper we study a quasilinear resonant problem with discontinuous right hand side. To develop an existence theory we pass to a multivalued version of the problem, by filling in the gaps at the discontinuity points. We prove the existence of a nontrivial solution using a variational approach based on the critical point theory of nonsmooth locally Lipschitz functionals.