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Semiclassical States of Nonlinear Schrödinger Equations

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Abstract.

The existence of semiclassical states to some nonlinear Schrödinger equations that concentrate near the critical points of the potential V is studied by means of a local approach, variational in nature. We also discuss stability and necessary conditions for concentration. The same method is used to find multiple homoclinic orbits to a class of second‐order Hamiltonian systems.

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(Accepted April 24, 1996)

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Ambrosetti, A., Badiale, M. & Cingolani, S. Semiclassical States of Nonlinear Schrödinger Equations. Arch Rational Mech Anal 140, 285–300 (1997). https://doi.org/10.1007/s002050050067

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