Isomorphism theorem for BSS recursively enumerable sets over real closed fields

AbstractThe main result of this paper lies in the framework of BSS computability: it shows roughly that any recursively enumerable set S in RN, N⩽∞, where R is a real closed field, is isomorphic to RdimS by a bijection ϕ which is decidable over S. Moreover the map S↦ϕ is computable. Some related matters are also considered like characterization of the real closed fields with a r.e. set of infinitesimals, and the dimension of r.e. sets

Noncompact variational problems: concentration at infinity, strong indefiniteness

Doctorat en sciences mathématiques -- UCL, 199

Nontrivial solution of a semilinear Schrodinger equation

This paper deals with strongly indefinite functionals whose gradients are Fredholm operators of index 0 and map weakly convergent sequences to weakly convergent sequences. We show bow these results apply to a Z(N)-invariant semilinear Schrodinger equation on R(N)

A non-variational system involving the critical Sobolev exponent. The radial case

In this paper we consider the non-variational system−Δui=Σj=1kaijujN+2N−2inRN,ui>0inRN,ui∈D1,2(RN),and we give some sufficient conditions on thematrix (aij)i, j =1,..,k which ensure the existence of solutions bifurcating from the bubble of the critical Sobolev equation

On the Mountain-pass algorithm for the quasi-linear Schrodinger equation

We compute the mountain pass solutions of a class of quasi-linear Schrodinger equation

Asymptotic symmetries for fractional operators

We study the symmetry properties of some nonlocal operator