Local Mountain Pass for a Class of Elliptic Systems without Homogeneity on the Nonlinearity
Keywords:
Gradient elliptic systems, Schrödinger equation.Abstract
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.
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