21 citations · 26 across the 7 of their papers we have counts for
6 papers · 1 filter
Faber-Krahn type inequalities and uniqueness of positive solutions on metric measure spaces
Anup Biswas, Janna Lierl
We consider a general class of metric measure spaces equipped with a regular Dirichlet form and then provide a lower bound on the hitting time probabilities of the associated Hunt…
Liouville type results for systems of equations involving fractional Laplacian in exterior domains
Anup Biswas
In this article we present a simple and unified probabilistic approach to prove nonexistence of positive super-solutions for systems of equations involving potential terms and the…
A variational formula for risk-sensitive control of diffusions in
Ari Arapostathis, Anup Biswas
We address the variational problem for the generalized principal eigenvalue on of linear and semilinear elliptic operators associated with nondegenerate diffusions c…
Existence and non-existence results for a class of semilinear nonlocal operators with exterior condition
Anup Biswas
We consider a class of semilinear nonlocal problems with vanishing exterior condition and establish a Ambrosetti-Prodi type phenomenon when the nonlinear term satisfies certain con…
Principal eigenvalues of a class of nonlinear integro-differential operators
Anup Biswas
We consider a class of nonlinear integro-differential operators and prove existence of two principal (half) eigenvalues in bounded smooth domains with exterior Dirichlet condition.…
Ambrosetti-Prodi type results for Dirichlet problems of fractional Laplacian-like operators
Anup Biswas, József Lőrinczi
We establish Ambrosetti--Prodi type results for viscosity and classical solutions of nonlinear Dirichlet problems for the fractional Laplace and comparable operators. In the choice…