Concepedia

Dispersive estimates for Schrödinger operators in the presence of a resonance and/or an eigenvalue at zero energy in dimension three: I

M. Burak Erdoğan, Wilhelm Schlag

Dynamics of Partial Differential Equations · 2004 · 106 citations · 34 references

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Abstract

We prove dispersive estimates for Schrdinger equations in three dimensions without making any assumptions on zero energy.

References

34

Nonlinear scalar field equations, I existence of a ground state

Henri Berestycki, P. L. Lions · Archive for Rational Mechanics and Analysis · 1983 · 2.6K citations · Full text

, , +13

Existence of solitary waves in higher dimensions

Walter A. Strauss · Communications in Mathematical Physics · 1977 · 1.8K citations

, , +11

Uniqueness of positive solutions of Δu−u+up=0 in Rn

Man Kam Kwong · Archive for Rational Mechanics and Analysis · 1989 · 1.3K citations

, , +10

Stability theory of solitary waves in the presence of symmetry, II

Manoussos G. Grillakis, Jalal Shatah, Walter A. Strauss · Journal of Functional Analysis · 1990 · 1.3K citations

, , +14

Orbital stability of standing waves for some nonlinear Schr�dinger equations

Thierry Cazenave, Pierre‐Louis Lions · Communications in Mathematical Physics · 1982 · 1.1K citations

, , +11