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math.AP2022
Existence of positive solutions for a parameter fractional -Laplacian problem with semipositone nonlinearity
Emer Lopera, Camila López, Raúl E. Vidal
In this paper we prove the existence of at least one positive solution for the nonlocal semipositone problem \[ \displaystyle \left\{\begin{array}{rcll} (-Δ)_p^s(u) &=& λf(u) \qqua…
math.AP2018
Nonlocal diffusion equations in Carnot Groups
Isolda Eugenia Cardoso, Raúl Emilio Vidal
Let be a Carnot group. We study nonlocal diffusion equations in a domain of of the form $$ u_t^ε(x,t)=\int_{G}\frac{1}{ε^2}K_ε(x,y)(u^ε(y,t)-u^ε(x,t))\,dy, \qquad x\in…
math.AP2017
Nonlocal heat equations in the Heisenberg group
Raúl Emilio Vidal
We study the following nonlocal diffusion equation in the Heisenberg group , \[ u_t(z,s,t)=J\ast u(z,s,t)-u(z,s,t), \] where denote convolution product and …