Article ID Journal Published Year Pages File Type
4604259 Annales de l'Institut Henri Poincare (C) Non Linear Analysis 2014 25 Pages PDF
Abstract

We study the existence of positive solutions on RN+1RN+1 to semilinear elliptic equation −Δu+u=f(u)−Δu+u=f(u) where N⩾1N⩾1 and f   is modeled on the power case f(u)=|u|p−1uf(u)=|u|p−1u. Denoting with c   the mountain pass level of V(u)=12‖u‖H1(RN)2−∫RNF(u)dx, u∈H1(RN)u∈H1(RN) (F(s)=∫0sf(t)dt), we show, via a new energy constrained variational argument, that for any b∈[0,c)b∈[0,c) there exists a positive bounded solution vb∈C2(RN+1)vb∈C2(RN+1) such that Evb(y)=12‖∂yvb(⋅,y)‖L2(RN)2−V(vb(⋅,y))=−b and v(x,y)→0v(x,y)→0 as |x|→+∞|x|→+∞ uniformly with respect to y∈Ry∈R. We also characterize the monotonicity, symmetry and periodicity properties of vbvb.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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