Geodesic
Local mountain pass for a class of elliptic systems without homogeneity on the nonlinearity
Minimax theory and its applications, Tome 8 (2023) no. 2
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We consider the gradient elliptic system given by −ε2div(a(x)∇u) + u = Qu(u,v)+λKu(u,v) in RN, −ε2div(b(x)∇v) + v = Qv(u,v)+λKv(u,v) in RN, where the potentials a,b are continuous, the nonlinearity Q+λK is not homogeneous. We study the subcritical, critical and supercritical cases. For ε > 0 small we show existence and concentration results using the penalization method.
Mots-clés : Gradient elliptic systems, Schrödinger equation 
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     author = {Giovany M. Figueiredo and Segundo Manuel A. Salirrosas},
     title = {Local mountain pass for a class of elliptic systems without homogeneity on the nonlinearity},
     journal = {Minimax theory and its applications},
     year = {2023},
     volume = {8},
     number = {2},
     zbl = {1529.35189},
     url = {http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a0/}
}
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Giovany M. Figueiredo; Segundo Manuel A. Salirrosas. Local mountain pass for a class of elliptic systems without homogeneity on the nonlinearity. Minimax theory and its applications, Tome 8 (2023) no. 2. http://geodesic.mathdoc.fr/item/MTA_2023_8_2_a0/