We consider the problem-triangle u + lambda u = |u|(p-2)u, where u is an element of H-0(1)(Omega) satisfies |u|(2) = m > 0, lambda is an element of R and Omega is a smooth exterior domain. We prove the existence of a positive solution with a constrained Morse index less or equal than N + 1 and lambda >= 0. We treat both the cases m fixed and R-N \ Omega small and Omega fixed and m large.
Appolloni, L., Molle, R. (2025). Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS [10.3934/dcds.2025120].
Normalized Schrödinger equations with mass-supercritical nonlinearity in exterior domains
Molle, R
2025-01-01
Abstract
We consider the problem-triangle u + lambda u = |u|(p-2)u, where u is an element of H-0(1)(Omega) satisfies |u|(2) = m > 0, lambda is an element of R and Omega is a smooth exterior domain. We prove the existence of a positive solution with a constrained Morse index less or equal than N + 1 and lambda >= 0. We treat both the cases m fixed and R-N \ Omega small and Omega fixed and m large.File in questo prodotto:
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