An energy constrained method for the existence of layered type solutions of NLS equations
Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 4, pp. 725-749.

We study the existence of positive solutions on N+1 to semilinear elliptic equation -Δu+u=f(u) where N1 and f is modeled on the power case f(u)=|u| p-1 u. Denoting with c the mountain pass level of V(u)=1 2u H 1 ( N ) 2 - N F(u)dx, uH 1 ( N ) (F(s)= 0 s f(t)dt), we show, via a new energy constrained variational argument, that for any b[0,c) there exists a positive bounded solution v b C 2 ( N+1 ) such that E v b (y)=1 2 y v b (·,y) L 2 ( N ) 2 -V(v b (·,y))=-b and v(x,y)0 as |x|+ uniformly with respect to y. We also characterize the monotonicity, symmetry and periodicity properties of v b .

DOI : 10.1016/j.anihpc.2013.07.003
Classification : 35J60, 35B08, 35B40, 35J20, 34C37
Mots clés : Semilinear elliptic equations, Locally compact case, Variational methods, Energy constraints
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     title = {An energy constrained method for the existence of layered type solutions of {NLS} equations},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {725--749},
     publisher = {Elsevier},
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Alessio, Francesca; Montecchiari, Piero. An energy constrained method for the existence of layered type solutions of NLS equations. Annales de l'I.H.P. Analyse non linéaire, Tome 31 (2014) no. 4, pp. 725-749. doi : 10.1016/j.anihpc.2013.07.003. http://www.numdam.org/articles/10.1016/j.anihpc.2013.07.003/

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