Bound states of the NLS equation on metric graphs with localized nonlinearities

By E. Serra, Lorenzo Tentarelli. 2015

62 citations recorded by the source corpus.

Abstract We investigate the existence of multiple bound states of prescribed mass for the nonlinear Schrodinger equation on a noncompact metric graph. The main feature is that the nonlinearity is localized only in a compact part of the graph. Our main result states that for every integer k , the equation possesses at least k solutions of prescribed mass, provided that the mass is large enough. These solutions arise as constrained critical points of the NLS energy functional. Estimates for the energy of the solutions are also established.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9d81eff8afad6efee58a9e97a9121cd977316dc6

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In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Existence of infinite stationary solutions of the $L^2$-subcritical and critical NLSE on compact metric graphs (2017, methodology): “ H1 µ(G), we deﬁne the quantity λ= λ(u) := − 1 µ E′(u)u= 1 µ Z G |u|pdx− Z G |u′|2dx (11) and the linear functional J(u) : H1(G) → R J(u)v:= Z G u′v′dx− Z G |u|p−2uvdx+λ Z G uvdx (12) As proved in [21] (Section 2), since {un}n∈N is a bounded Palais-Smale sequence, condition (ii) in Deﬁnition 2.2 ca”
Normalized solutions of $L^2$-supercritical NLS equations on compact metric graphs (2022, background): “We also refer the interested reader to [10, 14, 27, 28, 29, 31] and references therein for strictly related issues (problems with localized nonlinearities, combined nonlinearities, existence of critical points in absence of ground states), always in subcritical and critical regimes.”