Mervan Pašić

Localized Local Maxima for Non-Negative Ground State Solution of Nonlinear Schrödinger Equation with Non-Monotone External Potential

abstract:
A non-negative ground state solution $u(x)$ of the nonlinear Schrödinger equation with non-monotone potential is studied. The existence of local maxima of $u(x)$ which are attained on the given intervals in one-dimensional space variable $x$ is shown. Next, it is proved that the stationary point of $u(x)$ per one interval is unique. The co-existence of the local extrema of ground state solution and external potential on the same interval is considered, too.

Mathematics Subject Classification: 35Q55, 82-XX, 34C10, 34C15

Key words and phrases: Schrödinger equation, ground state solution, extrema, non-monotonic behaviour, particle density, Bose-Einstein condensates