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Branches of solutions for an asymptotically linear elliptic problem on RN

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DOI: 10.4236/ojapps.2012.24B043    1,295 Downloads   2,086 Views  
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ABSTRACT

We consider  the following nonlinear schr?dinger equation
-?u+λV(x)u=f(x,u)withu∈H^1 (R^N) and u?0,(*)
whereλ>0 and f(x,s) is asymptotically linear withrespect to sat origin and infinity. The potential V(x) satisfies V(x)≥V_0>0for all x∈R^N and (_|x|→+∞^lim)V(x)=V (∞)∈(0,+∞). We provethat problem (*) has two connected sets of positive and negative  solutions inR×W^(2,p) (R^N)for somep∈[2,+∞)∩(N/2,+∞).

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Wan, Y. (2012) Branches of solutions for an asymptotically linear elliptic problem on RN. Open Journal of Applied Sciences, 2, 187-194. doi: 10.4236/ojapps.2012.24B043.

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