凹凸性混合的非线性Schrdinger方程解的存在性定理

EXISTENCE THEOREM OF CONCAVE AND CONVEX EFFECTS FOR NONLINEAR SCHRDINGER EQUATIONS

讨论非线性Ｓｃｈｒｄｉｎｇｅｒ方程－Δｕ＋ｑ（ｘ）ｕ＝λｕ＋Ｐ（ｘ）｜ｕ｜ｐ－１ｕ＋Ｑ（ｘ）｜ｕ｜α－１ｕｘ∈ＲＮ的多解存在性，其中ｑ（ｘ）满足周期性，Ｐ（ｘ），Ｑ（ｘ）是满足一定条件的连续函数，λ∈Ｒ落在－Δ＋ｑ的谱隙（ｓｐｅｃｔｒａｌｇａｐ）中，０＜α＜Ｎ－２Ｎ＋２＜１＜ｐ＜Ｎ＋２Ｎ－２．

In this paper,we discuss existence of solutions for nonlinear Schrdinger equation -Δu+q(x)u=λu+P(x)|u| p-1 u+Q(x)|u| α-1 u\ x∈R N where q(x) is periodic,λ lies in a spectral gap of -Δ+q,P(x) and Q(x) is continuous functionals and 0<α<N-1N+2<1<p<N+2N-2.