We establish Ambrosetti–Prodi type results for viscosity and classical solutions of nonlinear Dirichlet problems for fractional Laplace and comparable operators. In the choice of nonlinearities we consider semi-linear and super-linear growth cases separately. We develop a new technique using a functional integration-based approach, which is more robust in the non-local context than a purely analytic treatment.
Published inIntegral Equations and Operator Theory
VersionVoR (Version of Record)
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DepositorDr Jozsef Lorinczi. Deposit date: 9 June 2020