Sufficient conditions for minima of some translation invariant functionals (Q1386244)

The question of a constrained minimization of a functional with a nonlocal convolutive term on the entire space is considered. It corresponds with the problem of nonnegative solutions of a nonlinear equation in \(R^N\), containing the Laplacian and a convolution operator. Instead of a strict subadditivity, used in the concentration-compactness method by \textit{P. L. Lions}, the author proposes another assumption to prove a precompactness of minimizing sequences. Functionals with two dependent variables and one constraint of isoperimetric type are also studied.