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math.AP2011
On a system involving a critically growing nonlinearity
Antonio Azzollini, Pietro d'Avenia
This paper deals with the system \[\{{array}{ll} -Δu = λu + q |u|^3 u ϕ& \hbox{in} B_R, -Δϕ=q |u|^5 & \hbox{in} B_R, u=ϕ=0 & \hbox{on} \partial B_R. {array}.\] We prove existence a…
math.AP2011★ 1 cited
Semi-classical states for the Nonlinear Schrödinger Equation on saddle points of the potential via variational methods
Pietro d'Avenia, Alessio Pomponio, David Ruiz
In this paper we study semiclassical states for the problem $$ -\eps^2 Δu + V(x) u = f(u) \qquad \hbox{in} \RN,$$ where is a superlinear nonlinear term. Under our hypotheses…