一类奇异摄动方程最小能量解的存在性

The Existence of a Least-energy Solution for a Singularly Perturbed Equation

考虑非线性奇异摄动方程-ε2Δu+u=f(u),u∈H01(Ω)最小能量解的存在性,这个解的存在性是在一个更弱的超二次条件下得到的,代替了通常超线性问题中使用的更强的Ambrosetti-Rabinwitz条件.

The existence of a least-energy solution of a singularly perturbed nonlinear elliptic equation-ε^2 Δ u＋u=f（u）,u∈H10（Ω）is considered.Prove the main results under a more weaker super-quadratic condition,instead of the standard Ambrosetti-Rabinwitz condition,which is usually used in super-linear problems.