TY - JOUR
T1 - Some vector field equations
AU - Lieb, Elliott H.
N1 - Funding Information:
* The author was partially supported by U. S. National Science Foundation Grant
PY - 1984/1/1
Y1 - 1984/1/1
N2 - Systems of the type −Δui = gi(u), with u = (u1,…,un) and gi(u) = ∂G/∂ui on Rd, d ≥ 2 are studied. Under suitable conditions on G and g it is shown that there is a solution of the system that also minimizes the action, S(u) = ∫|∇u|2 − ∫G(u) within the class of all nontrivial finite action solutions of the system.
AB - Systems of the type −Δui = gi(u), with u = (u1,…,un) and gi(u) = ∂G/∂ui on Rd, d ≥ 2 are studied. Under suitable conditions on G and g it is shown that there is a solution of the system that also minimizes the action, S(u) = ∫|∇u|2 − ∫G(u) within the class of all nontrivial finite action solutions of the system.
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U2 - 10.1016/S0304-0208(08)73722-8
DO - 10.1016/S0304-0208(08)73722-8
M3 - Article
AN - SCOPUS:77957294341
SN - 0304-0208
VL - 92
SP - 403
EP - 412
JO - North-Holland Mathematics Studies
JF - North-Holland Mathematics Studies
IS - C
ER -