外部区域上非线性椭圆问题正解的多解性

Multiplicity of Positive Solutions forNonlinear Elliptic Problems inExterior Domain

摘要: 研究了外部区域上非线性椭圆问题正解的多解性，其中Ω={x∈ ℝ^N: |x| > 1}, N ≥ 3, α > 0 为常数，n 表示 ∂Ω 上的单位法向量， f∈C([0,∞), [0, ∞)) 且f在0或∞处满足不同增长条件。 通过运用不动点指数理论获得了问题(P)的多解性结果。

Abstract: We are concerned with the multiplicity of positive solutions for nonlinear elliptic problems in exterior domain where Ω={x∈ ℝ^N: |x| > 1}, N ≥ 3, α > 0 is a constant, n denotes the outer unit normal vector on ∂Ω, and f∈C([0,∞), [0, ∞)) satisfies different growth conditions at zero and infinity. By using fixed point index theory, we obtain the multiplicity of positive solutions for problem (P).