TY - JOUR
T1 - Stability of bound states of Hamiltonian PDEs in the degenerate cases
AU - Maeda, Masaya
N1 - Funding Information:
The author wants to thank the helpful discussions with Professor Masahito Ohta. The author would also like to express his deep gratitude to Professor Yoshio Tsutsumi for his helpful comments. The author was partially supported by Grant-in-Aid for JSPS Fellows (20·56371). The author is grateful to the referee for reading the manuscript carefully and for giving valuable suggestions.
PY - 2012/7/15
Y1 - 2012/7/15
N2 - We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.
AB - We consider a Hamiltonian systems which is invariant under a one-parameter unitary group and give a criterion for the stability and instability of bound states for the degenerate case. We apply our theorem to the single power nonlinear Klein-Gordon equation and the double power nonlinear Schrödinger equation.
KW - Bound states
KW - Nonlinear Klein-Gordon equation
KW - Nonlinear Schrödinger equation
KW - Orbital stability
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U2 - 10.1016/j.jfa.2012.04.006
DO - 10.1016/j.jfa.2012.04.006
M3 - Article
AN - SCOPUS:84861345420
VL - 263
SP - 511
EP - 528
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 2
ER -