一类非线性椭圆障碍问题正解的存在性

Existence of Positive Solution for a Class of Nonlinear Elliptic Obstacle Problems

在一个有界区域Ω RN(N≥ 3)上讨论了一类非线性椭圆算子障碍问题在容许集合 Rψ={ v∈W1,p0 (Ω)∶ v≥ ψ a.e.inΩ}上正解的存在性 .利用泛涵的下半连续性、集中紧性原理以及变分方法等证明了障碍问题至少有一个正解 .

The existence of positive solution for a class of nonlinear elliptic obstacle problem was discussed on a bounded domain Ω R N(N≥3). By using the lower semi continuity of functional, concentration compact principle and variational principle etc., it was obtained that there is at least one positive solution for the obstacle problem.