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.
Keywords: mountain-pass theorem, variational methods, Nehari manifold, Brouwer degree, concentration-compactness
@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://www.numdam.org/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://www.numdam.org/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://www.numdam.org/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, Volume 12 (2006) no. 4, pp. 786-794. doi : 10.1051/cocv:2006022. http://www.numdam.org/articles/10.1051/cocv:2006022/
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