Ambrosetti-Prodi type results for Dirichlet problems of fractional Laplacian-like operators
Anup Biswas
Jozsef Lorinczi
2134/12452408.v1
https://repository.lboro.ac.uk/articles/journal_contribution/Ambrosetti-Prodi_type_results_for_Dirichlet_problems_of_fractional_Laplacian-like_operators/12452408
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.
2020-06-09 13:30:21
Semi-linear nonlocal exterior value problem
Ambrosetti–Prodi problem
Viscosity solutions
Bifurcations
Fractional Schrödinger operator
Principal eigenvalues
Maximum principles