Juan Dávila

Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations

We investigate stable solutions of elliptic equations of the type where n ≥ 2, s ∈ (0, 1), λ ≥0 and f is any smooth positive superlinear function. The operator (− Δ) s stands for the fractional Laplacian, a pseudo-differential operator of order 2s. According to the value of λ, we study the existence and regularity of weak solutions u.

Nonlocal anisotropic dispersal with monostable nonlinearity

Abstract We study the travelling wave problem J ⋆ u − u − c u ′ + f ( u ) = 0 in R , u ( − ∞ ) = 0 , u ( + ∞ ) = 1 with an asymmetric kernel J and a monostable nonlinearity. We prove the existence of a minimal speed, and under certain hypothesis the uniqueness of the profile for c ≠ 0 . For c = 0 we show examples of nonuniqueness.

Existence and Uniqueness of Solutions to a Nonlocal Equation with Monostable Nonlinearity

Let

STABLE SOLUTIONS FOR THE BILAPLACIAN WITH EXPONENTIAL NONLINEARITY.

J \in C(\mathbb{R})

Pulsating fronts for nonlocal dispersion and KPP nonlinearity

,

Hardy-type inequalities

J\ge 0

Nondegeneracy of the bubble in the critical case for nonlocal equations

,

Positive versus free boundary solutions to a singular elliptic equation

\int_{\mbox{\tinyR}} J = 1

Existence and asymptotic behavior for a singular parabolic equation

and consider the nonlocal diffusion operator

The Supercritical Lane-Emden-Fowler Equation in Exterior Domains

\mathcal{M}[u] = J \star u - u