Voir la notice de l'article provenant de la source Numdam
An elliptic PDE is studied which is a perturbation of an autonomous equation. The existence of a nontrivial solution is proven via variational methods. The domain of the equation is unbounded, which imposes a lack of compactness on the variational problem. In addition, a popular monotonicity condition on the nonlinearity is not assumed. In an earlier paper with this assumption, a solution was obtained using a simple application of topological (Brouwer) degree. Here, a more subtle degree theory argument must be used.
@article{COCV_2006__12_4_786_0,
author = {Spradlin, Gregory S.},
title = {An elliptic equation with no monotonicity condition on the nonlinearity},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
pages = {786--794},
publisher = {EDP-Sciences},
volume = {12},
number = {4},
year = {2006},
doi = {10.1051/cocv:2006022},
mrnumber = {2266818},
zbl = {1123.35021},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006022/}
}
TY - JOUR AU - Spradlin, Gregory S. TI - An elliptic equation with no monotonicity condition on the nonlinearity JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2006 SP - 786 EP - 794 VL - 12 IS - 4 PB - EDP-Sciences UR - http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006022/ DO - 10.1051/cocv:2006022 LA - en ID - COCV_2006__12_4_786_0 ER -
%0 Journal Article %A Spradlin, Gregory S. %T An elliptic equation with no monotonicity condition on the nonlinearity %J ESAIM: Control, Optimisation and Calculus of Variations %D 2006 %P 786-794 %V 12 %N 4 %I EDP-Sciences %U http://geodesic.mathdoc.fr/articles/10.1051/cocv:2006022/ %R 10.1051/cocv:2006022 %G en %F COCV_2006__12_4_786_0
Spradlin, Gregory S. An elliptic equation with no monotonicity condition on the nonlinearity. ESAIM: Control, Optimisation and Calculus of Variations, Tome 12 (2006) no. 4, pp. 786-794. doi: 10.1051/cocv:2006022
Cité par Sources :