带临界指数的Kirchhoff型线性耦合方程组正解的多重性

该文研究了如下带Sobolev临界指数的Kirchhoff型线性耦合方程组{−(1+b_(1)∥u∥^(2))Δu+λ_(1)u=u5+βv,x∈Ω,−(1+b_(2)∥v∥^(2))Δv+λ_(2)v=v^(5)+βu,x∈Ω,u=v=0在∂Ω上,其中Ω⊂R^(3)是一个开球,∥⋅∥表示H_(0)^(1)(Ω)的范数,β∈R是一个耦合参数.常数b_(i)≥0和λ_(i)∈(−λ_(1)(Ω),−1/4λ_(1)(Ω)),i=1,2,这里λ_(1)(Ω)是(−Δ,H_(0)^(1)(Ω))的第一特征值.在含有Kirchhoff项的情形下,利用变分法证明了方程组有一个正基态解和一个高能量的正解,并研究了当β→0时这两个解的渐近行为.

EXISTENCE OF SOLUTIONS FOR QUASILINEAR ELLIPTIC EQUATIONS WITH UNBOUNDED COEFFICIENTS ON RN

In this paper a class of p-Laplace type elliptic equations with unbounded coefficients on RN is considered. It is proved that there exist radial solutions on RN. On sufficiently large ball, radial and nonradial solutions are obtained. Finally, some necessary conditions for the existence of solutions are given.

On Existence of Ground States for Some Elliptic Systems

In this paper we consider the existence of ground states for some 2- coupled nonlinear Schrodinger systems with or without potentials. Under various conditions on the parameters in the equations, we prove the existence of ground states.