In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.
In this article,we consider the existence of positive solutions for weakly cou-pled nonlinear elliptic systems {-△u+u (1+a(x))|u| p-1 u+μ|u| α-2 u|v|β+λv in R^N,-△v+v=(1+bx))|v|p-1v+μ|u|α|v|β-2v+λu in R N.(0.1) To find nontrivial solutions,we first investigate autonomous systems.In this case,results of bifurcation from semi-trivial solutions are obtained by the implicit function theorem.Next,the existence of positive solutions of problem(0.1) is obtained by variational methods.
认为下列 Neumann 问题是在哪儿的(*) d >
0， B 1 是在 ℝ
N , k (x)= 的联合起来的球 k (|x|)≢
0 是非否定的并且在里面与 N ≥
3。它被显示出在[2 ] 那任何 d >
0，问题(*) 没有非经常的放射状地对称的最少的精力答案如果 k (x)≡
1。由我们证明那的一条含蓄的功能定理，有 d 0>
0 以便(*) 有一个唯一的放射状地对称的最少的精力答案如果这个答案是的 d >
d 0, 经常如果 k (x)≡
1 并且非经常如果 k (x)≢
1。特别地，为 k (x)≡
1， d 0 能明确地被表示。
The main purpose of this paper is to analyze the asymptotic behavior of the radial solution of Hénon equation △ u = |x|αup-1, u > 0, x ∈ BR(0) Rn (n 3), u = 0, x ∈ BR(0), where p → p(α) = 2(n+α)/n-2 from left side, α > 0.
The authors consider the semilinear Schrdinger equation -△Au + Vλ(x)u = Q(x)|u|γ-2u in RN, where 1 < γ < 2* and γ = 2, Vλ = V + - λV -. Exploiting the relation between the Nehari manifold and fibrering maps, the existence of nontrivial solutions for the problem is discussed.
The authors prove the existence of nontrivial solutions for the Schrdinger equation -△u + V (x)u = λf(x, u) in RN,where f is superlinear, subcritical and critical at infinity, respectively, V is periodic.
