In this paper we prove the existence of ground state solutions of the modified nonlinear Schro ̈dinger equation: −u+V(x)u−21uu2 =|u|p−1u, x∈RN, N≥3, under some hypotheses on V (x). This model has been proposed in the theory of superfluid films in plasma physics. As a main novelty with respect to some previous results, we are able to deal with exponents p ∈ (1, 3). The proof is accomplished by minimization under a convenient constraint.
Existence of ground states for a modified nonlinear Schrodinger equation
Siciliano, Gaetano
2009-01-01
Abstract
In this paper we prove the existence of ground state solutions of the modified nonlinear Schro ̈dinger equation: −u+V(x)u−21uu2 =|u|p−1u, x∈RN, N≥3, under some hypotheses on V (x). This model has been proposed in the theory of superfluid films in plasma physics. As a main novelty with respect to some previous results, we are able to deal with exponents p ∈ (1, 3). The proof is accomplished by minimization under a convenient constraint.File in questo prodotto:
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