Energy critical fourth-order Schrödinger equations with subcritical perturbations

DOI10.1016/j.na.2010.04.027zbMath1192.35168OpenAlexW1972269008MaRDI QIDQ984070

Ji Qiang Zheng, Jun Yong Zhang

Publication date: 13 July 2010

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.04.027

zbMATH Keywords

scatteringglobal well-posednessfourth-order Schrödinger equationStrichartz-type estimate

Mathematics Subject Classification ID

Scattering theory for PDEs (35P25) A priori estimates in context of PDEs (35B45) NLS equations (nonlinear Schrödinger equations) (35Q55) PDEs in connection with quantum mechanics (35Q40)

Related Items (10)

The asymptotic property for nonlinear fourth-order Schrödinger equation with gain or loss ⋮ Unconditional uniqueness of solution for \(\dot{H}^{s_c}\) critical 4th order NLS in high dimensions ⋮ Normalized solutions to biharmonic Schrödinger equation with critical growth in \(\mathbb{R}^N\) ⋮ Existence and multiplicity of normalized solutions to biharmonic Schrödinger equations with subcritical growth ⋮ Global existence and asymptotic behavior of the Cauchy problem for fourth-order Schrödinger equations with combined power-type nonlinearities ⋮ The property of the solution about Cauchy problem for fourth-order Schrödinger equation with critical time-oscillating nonlinearity ⋮ Asymptotics for the fourth-order nonlinear Schrödinger equation in the critical case ⋮ The initial-boundary value problem for the biharmonic Schrödinger equation on the half-line ⋮ On the well-posedness and stability for the fourth-order Schrödinger equation with nonlinear derivative term ⋮ Normalized ground states of nonlinear biharmonic Schrödinger equations with Sobolev critical growth and combined nonlinearities

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