Nonexistence of Positive Solutions for Quasilinear Equations with Decaying Potentials

In this paper, we consider a quasilinear Schrödinger equation, which arises from the study of the superfluid film equation in plasma physics. Our main goal is to find the growth condition for nonlinear term and decaying condition for the potential, which guarantee the nonexistence of positive solutions.

A MATHEMATICAL VERIFICATION OF THE EXISTENCE OF STRINGS OF CIRCULATION IN SUPERFLUID FILMS ON POROUS MEDIA

A superfluid film flowing along the walls of a porous material can be modeled by a harmonic differential on a punctured Riemann surface satisfying integrality conditions on its periods and residues. In this paper, we use classical Riemann surface theory to mathematically investigate the observed physical phenomenon of the appearance of pairs of vortices in the fluid and the resulting patterns of circulation. We show that the existence of strings of circulation in the superfluid depends on a quantized divisibility condition between the number of vortex–antivortex pairs and the circulation of the fluid.