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We consider the existence of multiple positive solutions to the nonlinear Schrodinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will… Click to show full abstract
We consider the existence of multiple positive solutions to the nonlinear Schrodinger systems set on , under the constraint Here are prescribed, , and the frequencies are unknown and will appear as Lagrange multipliers. Two cases are studied, the first when , the second when In both cases, assuming that is sufficiently small, we prove the existence of two positive solutions. The first one is a local minimizer for which we establish the compactness of the minimizing sequences and also discuss the orbital stability of the associated standing waves. The second solution is obtained through a constrained mountain pass and a constrained linking respectively.
Journal Title: Nonlinearity
Year Published: 2018
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