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Stationary solutions of the nonlinear Schrödinger equation with fast-decay potentials concentrating around local maxima
Jonathan Di Cosmo, Jean Van Schaftingen
We study positive bound states for the equation where is a real parameter, a…
Existence, stability and oscillation properties of slow decay positive solutions of supercritical elliptic equations with Hardy potential
Vitaly Moroz, Jean Van Schaftingen
We prove the existence of a family of slow decay positive solutions of a supercritical elliptic equation with Hardy potential in the entire space and study stability and oscillatio…
Finding critical points whose polarization is also a critical point
Marco Squassina, Jean Van Schaftingen
We show that near any given minimizing sequence of paths for the mountain pass lemma, there exists a critical point whose polarization is also a critical point. This is motivated b…
Limiting Sobolev inequalities for vector fields and canceling linear differential operators
Jean Van Schaftingen
The estimate [\lVert D^{k-1}u\rVert_{L^{n/(n-1)}} \le \lVert A(D)u \rVert_{L^1} ] is shown to hold if and only if (A(D)) is elliptic and canceling. Here (A(D)) is a homogeneous lin…