We find for small Îµ positive solutions to the equation âˆ’div (|x| âˆ’2a âˆ‡u) âˆ’ Î» |x| 2(1+a) u = 1 + Îµk(x) u pâˆ’1 |x| bp in R N , which branch off from the manifold of minimizers in the class of radialâ€¦ (More)

This paper is devoted to the study of a problem arising from a geometric context, namely the conformal deformation of a Riemannian metric to a scalar flat one having constant mean curvature on theâ€¦ (More)

Positivity, essential self-adjointness, and spectral properties of a class of SchrÃ¶dinger operators with multipolar inverse-square potentials are discussed. In particular a necessary and sufficientâ€¦ (More)

In this paper we prescribe a fourth order conformal invariant on the standard n-sphere, with nâ‰¥5 , and study the related fourth order elliptic equation. We first find some existence results in theâ€¦ (More)

We deal with strongly competing multispecies systems of Lotka-Volâ€“ terra type with homogeneous Dirichlet boundary conditions. We show that the shape of the spatial domain contributes to theâ€¦ (More)

We deal with strongly competing multispecies systems of Lotka-Volterra type with homogeneous Neumann boundary conditions in dumbbell-like domains. Under suitable non-degeneracy assumptions, we showâ€¦ (More)

Asymptotics of solutions to SchrÃ¶dinger equations with singular magnetic and electric potentials is investigated. By using a Almgren type monotonicity formula, separation of variables, and anâ€¦ (More)

A theorem of Escobar asserts that, on a positive three dimensional smooth compact Riemannian manifold with boundary which is not conformally equivalent to the standard three dimensional ball, aâ€¦ (More)

We study positivity, localization of binding and essential self-adjointness properties of a class of SchrÃ¶dinger operators with many anisotropic inverse square singularities, including the case ofâ€¦ (More)