We study the following Schrodinger-Poisson system where (Pλ){-△u+ V(x)u+λФ(x)u^p=x∈R^3,-△Ф=u^2,lim│x│→∞Ф(x) =0,u〉0,where λ≥0 is a parameter,1 〈 p 〈 +∞, V(x) and Q(x)=1 ,D.Ruiz[19] prov...
For the following elliptic problem {-△u-μu/|x|^2=|u|^2^*(s)-2u/|x|^s+h(x), on R^N u∈D^1,2(R^N), N≥3, 0≤μ〈μ^-=(N-2)^2/4, 0≤s〈2, where 2^*(s)=2(N-s)/N-2 is the critical Sobolev-Hardy expon...
Let f(x, t): R2×R→ R be a C2-function with respect to t∈R, f(x,0) =0, f(x, t) ~ebt2 as t→+∞ for somc b>0. Under suitable conditions on f(x, t), author shows that for g∈L2 (R2), g(x)≥ 0, the following semilinear...