TITLE:
Branches of solutions for an asymptotically linear elliptic problem on RN
AUTHORS:
Youyan Wan
KEYWORDS:
Bifurcation, asymptotically linear, Fredholm opera- tor of index zero
JOURNAL NAME:
Open Journal of Applied Sciences,
Vol.2 No.4B,
January
16,
2013
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,+∞).