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Pure Mathematics 2024
外部区域上非线性椭圆问题正解的多解性
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Abstract:
研究了外部区域上非线性椭圆问题![\"\"](\"Edit_6029b701-86e4-47d4-b10e-1bdc276a50c6.png\")
正解的多解性，其中？={x∈ ？N: |x| > 1}, N ≥ 3, α > 0 为常数，n 表示 ？？ 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。
We are concerned with the multiplicity of positive solutions for nonlinear elliptic
problems in exterior domain ![\"\"](\"Edit_c8b586c7-bfde-4fcb-9545-6e00e8e537c6.png\")
where ？={x∈ ？N: |x| > 1}, N ≥ 3, α > 0 is a constant, n denotes the outer unit normal vector on ？？, 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).
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