Abstract. We consider the problemwhere Ω is an exterior domain inUnder symmetry assumptions on Ω and W, which allow finite symmetries, and some assumptions on the decay of W at infinity, we establish the existence of a positive solution and multiple sign changing solutions to this problem, having small energy.

We consider the problem−Δu + (Vwhere Ω is an exterior domain in ℝ

We consider the problem ∆u + λu + u 5 = 0, u > 0, in a smooth bounded domain Ω in R 3 , under zero Dirichlet boundary conditions. We obtain solutions to this problem exhibiting multiple bubbling behavior at k different points of the domain as λ tends to a special positive value λ 0 , which we characterize in terms of the Green function of −∆ − λ.

Artículo de publicación ISIWe consider the stationary nonlinear magnetic Choquard equation where is a magnetic potential and is a bounded electric potential. For a given group of linear isometries of , we assume that A(gx) = gA(x) and W(gx) = W(x) for all . Under some assumptions on the decay of A and W at infinity, we establish the existence of solutions to this problem which satisfy where is a given continuous group homomorphism into the unit complex numbers.Fondecyt (Chile) 314053

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