A general cone decomposition theory based on efficiency

1994 ◽  
Vol 65 (1-3) ◽  
pp. 1-20 ◽  
Author(s):  
J. E. Martínez-Legaz ◽  
A. Seeger
Keyword(s):  
Decomposition Theory ◽  
Cone Decomposition

scholarly journals DETERMINING EQUATIONS FOR HIGHER-ORDER DECOMPOSITIONS OF EXPONENTIAL OPERATORS

1995 ◽  
Vol 09 (25) ◽  
pp. 3241-3268 ◽  
Author(s):  
ZENGO TSUBOI ◽  
MASUO SUZUKI
Keyword(s):  
General Scheme ◽  
Higher Order ◽  
Explicit Formulas ◽  
Decomposition Theory ◽  
Lyndon Words

The general decomposition theory of exponential operators is briefly reviewed. A general scheme to construct independent determining equations for the relevant decomposition parameters is proposed using Lyndon words. Explicit formulas of the coefficients are derived.

scholarly journals Blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation

2020 ◽  
Vol 10 (1) ◽  
pp. 311-330 ◽  
Author(s):  
Feng Binhua ◽  
Ruipeng Chen ◽  
Jiayin Liu
Keyword(s):  
Blow Up ◽  
Standing Waves ◽  
Radial Solutions ◽  
Choquard Equation ◽  
Decomposition Theory ◽  
Profile Decomposition ◽  
Strong Instability

Abstract In this paper, we study blow-up criteria and instability of normalized standing waves for the fractional Schrödinger-Choquard equation $$\begin{array}{} \displaystyle i\partial_t\psi- (-{\it\Delta})^s \psi+(I_\alpha \ast |\psi|^{p})|\psi|^{p-2}\psi=0. \end{array}$$ By using localized virial estimates, we firstly establish general blow-up criteria for non-radial solutions in both L2-critical and L2-supercritical cases. Then, we show existence of normalized standing waves by using the profile decomposition theory in Hs. Combining these results, we study the strong instability of normalized standing waves. Our obtained results greatly improve earlier results.

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