We study the following nonlinear Schrödinger equation with a fourth-order dispersion term Δ2u−βΔu=g(u)in RN in the positive and zero mass regimes: in the former, N ⩾ 2 and β > −2√m, where m > 0 depends on g; in the latter, N ⩾ 3 and β > 0. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about g; if N = 2 in the positive mass case, or N = 4 in the zero mass case, we need to strengthen such assumptions. Our approach is variational.
Radial and non-radial multiple solutions to a general mixed dispersion NLS equation / D'Avenia, Pietro; Pomponio, Alessio; Schino, Jacopo. - In: NONLINEARITY. - ISSN 0951-7715. - STAMPA. - 36:3(2023), pp. 1743-1775. [10.1088/1361-6544/acb62d]
Radial and non-radial multiple solutions to a general mixed dispersion NLS equation
d'Avenia, Pietro;Pomponio, Alessio;
2023-01-01
Abstract
We study the following nonlinear Schrödinger equation with a fourth-order dispersion term Δ2u−βΔu=g(u)in RN in the positive and zero mass regimes: in the former, N ⩾ 2 and β > −2√m, where m > 0 depends on g; in the latter, N ⩾ 3 and β > 0. In either regimes, we find an infinite sequence of solutions under rather generic assumptions about g; if N = 2 in the positive mass case, or N = 4 in the zero mass case, we need to strengthen such assumptions. Our approach is variational.| File | Dimensione | Formato | |
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