具有强Allee效应的半线性椭圆方程正解的存在性和非存在性

基金项目: 国家自然科学基金资助项目(10671049);美国国家自然科学基金资助项目(NSFDMS-0314736)

Existence and Nonexistence of Positive Solutions of Semilinear Elliptic Equation With Inhomogeneous Strong Allee Effect

Y.Y.Tseng Functional Analysis Research Center and Department of Mathematics, Harbin Normal University, Harbin 150025, P. R. China;

摘要: 研究一个定义在有界光滑区域上的半线性椭圆方程解的问题，这类问题是在对空间生物种群模型的研究中出现的，其中的增长函数具有强Allee效应而且是非齐次的〖CX4〗．〖CX〗用变分方法证得，在这个有界光滑区域的一个开集上，如果满足一定条件，那么对足够大的参数，方程至少有两个正解，同时也得到一些非存在性结果
- 半线性椭圆方程 /
- Allee效应 /
- 正解 /
- 存在性
Abstract: A semilinear elliptic equation defined on a bounded smooth domain is studied. This type of problem arises from the studies of spatial ecology model, and the growth function in the equation was of strong Allee effect and inhom ogeneous. It was proved by variational methods that the equation has at least two positive solutions for a large parameter if it satisfies some appropriate conditions. Some nonexistence results were also proved.
- semilinear equation /
- Allee effect /
- positive solutions /
- existence

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