Resumen de Normalized Solutions for Schrödinger Equations with Local Superlinear Nonlinearities
Qin Xu, Gui-Dong Li, Shengda Zeng
In this paper, we consider the following Schrödinger equation:
where , , , and appears as a Lagrange multiplier. Assume that the nonlinear term f satisfies conditions only in a neighborhood of zero. For f has a subcritical growth, we prove the existence of the positive normalized solution for the equation with sufficiently small . For f has a supercritical growth, we derive the existence of the positive normalized solution for the equation with large enough. In addition, we also obtain infinitely many normalized solutions with sufficiently small for the subcritical case.
