The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.

Dancer, E. N.; Lam, Kee Y.; Yan, Shusen

Displaying similar documents to “The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrödinger equations.”

Multi-peak solutions for magnetic NLS equations without non-degeneracy conditions

Silvia Cingolani, Louis Jeanjean, Simone Secchi (2009)

ESAIM: Control, Optimisation and Calculus of Variations

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In this work we consider the magnetic NLS equation ${(\frac{ℏ}{i} \nabla - A (x))}^{2} u + V (x) u - {f (| u |}^{2}) u = 0 in ℝ^{N} (0.1)$ where $N \geq 3$ , $A : ℝ^{N} \to ℝ^{N}$ is a magnetic potential, possibly unbounded, $V : ℝ^{N} \to ℝ$ is a multi-well electric potential, which can vanish somewhere, $f$ is a subcritical nonlinear term. We prove the existence of a semiclassical multi-peak solution $u : ℝ^{N} \to ℂ$ to (0.1), under conditions on the nonlinearity which are nearly optimal.

Error estimates for scalar conservation laws by a kinetic approach.

Omrane, A. (2006)

International Journal of Mathematics and Mathematical Sciences

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Solvability of Kolmogorov-Fokker-Planck equations for vectorjump processes and occupation time on hypersurfaces.

Dokuchaev, N. G. (2001)

International Journal of Mathematics and Mathematical Sciences

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Spikes in two coupled nonlinear Schrödinger equations

Tai-Chia Lin, Juncheng Wei (2005)

Annales de l'I.H.P. Analyse non linéaire

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