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The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential
,
is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.
Xing Cheng, and Yanfang Gao. "Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential." Colloquium Mathematicae 134.1 (2014): 143-149. <http://eudml.org/doc/284377>.
@article{XingCheng2014, abstract = {The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential
$i∂_t u + 1/2 Δu - 1/2 |x|²u = -|u|^\{4/(d-2)\}u, x ∈ ℝ^\{d\}$,
is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up.}, author = {Xing Cheng, Yanfang Gao}, journal = {Colloquium Mathematicae}, keywords = {nonlinear Schrödinger equation; energy-critical; harmonic potential; blow-up}, language = {eng}, number = {1}, pages = {143-149}, title = {Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential}, url = {http://eudml.org/doc/284377}, volume = {134}, year = {2014}, }
TY - JOUR AU - Xing Cheng AU - Yanfang Gao TI - Blow-up for the focusing energy critical nonlinear Schrödinger equation with confining harmonic potential JO - Colloquium Mathematicae PY - 2014 VL - 134 IS - 1 SP - 143 EP - 149 AB - The focusing nonlinear Schrödinger equation (NLS) with confining harmonic potential
$i∂_t u + 1/2 Δu - 1/2 |x|²u = -|u|^{4/(d-2)}u, x ∈ ℝ^{d}$,
is considered. By modifying a variational technique, we shall give a sufficient condition under which the corresponding solution blows up. LA - eng KW - nonlinear Schrödinger equation; energy-critical; harmonic potential; blow-up UR - http://eudml.org/doc/284377 ER -