Gradient Flow Approach to the Calculation of Stationary States on Nonlinear Quantum Graphs

Furthermore, when relative compactness up to translations can be proved for any minimizing sequence, it can also be stated that the minimizing steady state solution is orbitally

Under a Nehari type condition, we show that the standard Ambrosetti–Rabinowitz super-linear condition can be replaced by a more natural super-quadratic condition.. © 2006

COLIN, On the Cauchy Problem for a Nonlocal, Nonlinear Schrödinger Equation Occuring in Plasma Physics, Differential and Integral Equations, Vol. STRAUSS,

, On smoothing property of Schr¨ odinger propagators, in Functional- Analytic Methods for Partial Differential Equations (Tokyo, 1989 ), Lecture Notes in Math.. , Smoothing property

We study relations between the ground-state energy of a quantum graph Hamiltonian with attractive δ coupling at the vertices and the graph geometry.. We derive a necessary and

[11] A. Grünrock, Bi- and trilinear Schrödinger estimates in one space dimension with applications to cubic NLS and DNLS, International Mathematics Research Notices, 41 ,

[1] T. Aubin, Prol` emes isop´ erim´ etriques et espaces de Sobolev, J. Mizutani, Uniform resolvent and Strichartz estimates for Schr¨ odinger equations with critical singularities,

As for (mNLS), the study of blowup solution to the focusing mass-critical nonlinear fractional Schr¨ odinger equation is closely related to the notion of ground state which is