一类渐近3-线性修正Schrodinger方程的正解

Positive Solutions for a Class of Modified Schrodinger Equations with an Asymptotically 3-Linear Term

运用山路引理和Lions引理,通过变量替换,得到了一类修正Schr?dinger方程-Δu+V(x)u-Δ(u2)u=g(x,u)x∈R^3正解的存在性.其中,当u→+∞时,g是渐近3-线性的.

Using the method of variable substitution,and based on the mountain pass lemma and Lions lemma,the existence of a positive solution is established for a modified Schr？ dinger equation-Δu＋V（x）u-Δ（u2）u=g（x,u） x ∈ R^3 and the nonlinear termgis asymptotically 3-linear as u→＋∞.