# Multi-peak positive solutions for nonlinear Schrï¿½dinger equations with critical frequency

## Related Articles

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For elliptic equations Îµ2Î” u âˆ’ V( x) u + f( u) = 0, x âˆˆ R N , N â‰§ 3, we develop a new variational approach to construct localized positive solutions which concentrate at an isolated component of positive local minimum points of V, as Îµ â†’ 0, under conditions on...

- Energy Growth in Schrï¿½dinger's Equation with Markovian Forcing. Erdo>ilde;an, M. Burak; Killip, Rowan; Schlag, Wilhelm // Communications in Mathematical Physics;Sep2003, Vol. 240 Issue 1/2, p1
Schrï¿½dinger's equation is considered on a one-dimensional torus with time dependent potential v(?,t)=?V(?)X(t), where V(?) is an even trigonometric polynomial and X(t) is a stationary Markov process. It is shown that when the coupling constant ? is sufficiently small, the average kinetic...

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We investigate the six-dimensional SchrÃ¶dinger equation for a three-body system with central pair interactions of a more general form than Coulomb interactions. Regular general and special physical solutions of this equation are represented by infinite asymptotic series in integer powers of...

- The Cauchy problem for quasi-linear SchrÃ¶dinger equations. Kenig, Carlos E.; Ponce, Gustavo; Vega, Luis // Inventiones Mathematicae;Nov2004, Vol. 158 Issue 2, p343
Studies the cauchy problem for quasi-linear schrodinger equations. Establishment of theorem A through artificial viscosity method; Examination of the linear elliptic equation; Calculations for linear estimates required for the proof of theorem A.

- Splitting Integrators for Nonlinear Schrï¿½dinger Equations Over Long Times. Gauckler, Ludwig; Lubich, Christian // Foundations of Computational Mathematics;Jun2010, Vol. 10 Issue 3, p275
Conservation properties of a full discretization via a spectral semi-discretization in space and a Lieï¿½Trotter splitting in time for cubic Schrï¿½dinger equations with small initial data (or small nonlinearity) are studied. The approximate conservation of the actions of the linear...

- On the Asymptotic Stability of Bound States in 2D Cubic Schrï¿½dinger Equation. Kirr, E.; Zarnescu, A. // Communications in Mathematical Physics;May2007, Vol. 272 Issue 2, p443
We consider the cubic nonlinear Schrï¿½dinger equation in two space dimensions with an attractive potential. We study the asymptotic stability of the nonlinear bound states, i.e. periodic in time localized in space solutions. Our result shows that all solutions with small, localized in space...

- Convergence of Logarithmic Quantum Mechanics to the Linear One. G�rka, Przemyslaw // Letters in Mathematical Physics;Sep2007, Vol. 81 Issue 3, p253
We study the nonlinear logarithmic Schrï¿½dinger equation in three dimensions. We establish the existence of the solutions of general quasi-linear Schrï¿½dinger equations. Finally, we show the convergence of the logarithmic quantum mechanics to the linear regime.

- Bound states for semilinear Schrï¿½dinger equations with sign-changing potential. Ding, Yanheng; Szulkin, Andrzej // Calculus of Variations & Partial Differential Equations;Jul2007, Vol. 29 Issue 3, p397
We study the existence and the number of decaying solutions for the semilinear Schrï¿½dinger equations $${-\varepsilon^{2}\Delta u + V(x)u = g(x,u)}$$ , $${\varepsilon > 0}$$ small, and $${-\Delta u + \lambda V(x)u = g(x,u)}$$ , $${\lambda > 0}$$ large. The potential V may change sign and g...

- Existence and concentration of ground states of coupled nonlinear Schrï¿½dinger equations with bounded potentials. Wei, Gongming // Chinese Annals of Mathematics;Jun2008, Vol. 29 Issue 3, p247
A 2-coupled nonlinear Schrï¿½dinger equations with bounded varying potentials and strongly attractive interactions is considered. When the attractive interaction is strong enough, the existence of a ground state for sufficiently small Planck constant is proved. As the Planck constant...