Journal
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES B
Volume 18, Issue 5, Pages 1155-1188Publisher
AMER INST MATHEMATICAL SCIENCES-AIMS
DOI: 10.3934/dcdsb.2013.18.1155
Keywords
Nonlinear Schrodinger equation; point interactions; ground states; concentration-compactness; solvable models
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Funding
- project PRIN
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We investigate the ground states of the one-dimensional nonlinear Schrodinger equation with a defect located at a fixed point. The nonlinearity is focusing and consists of a subcritical power. The notion of ground state can be defined in several (often non-equivalent) ways. We define a ground state as a minimizer of the energy functional among the functions endowed with the same mass. This is the physically meaningful definition in the main fields of application of NLS. In this context we prove an abstract theorem that revisits the concentration-compactness method and which is suitable to treat NLS with inhomogeneities. Then we apply it to three models, describing three different kinds of defect: delta potential, delta prime interaction, and dipole. In the three cases we explicitly compute ground states and we show their orbital stability.
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