具有收获的Logistic扩散方程的分支曲线与第一特征函数正交
Bifurcation curves of a diffusive logistic equation with harvesting orthogonal to the first eigenfunction
摘要：
研究了一类扩散Logistic方程的全局分支曲线，当收获与Laplacian的第一特征函数正交时，当线性增长率达到$λ_2+δ$时，详细考察了它们在线性增长率越过前两个特征值时的行为.我们观察到一些新的行为与早期的作品有关这个方程。即分歧曲线在$λ_1$处发生了变换，在$λ_1$之上是紧的，在$λ_2$之下存在两个Morse指数为零的退化解族，而在$λ_2$之下的解集不是二维流形.
英文摘要：
We study the global bifurcation curves of a diffusive logistic equation, when harvesting is orthogonal to the first eigenfunction of the Laplacian, for values of the linear growth up to $λ_2+δ$, examining in detail their behavior as the linear growth rate crosses the first two eigenvalues. We observe some new behavior with regard to earlier works concerning this equation. Namely, the bifurcation curves suffer a transformation at $λ_1$, they are compact above $λ_1$, there are precisely two families of degenerate solutions with Morse index equal to zero, and the whole set of solutions below $λ_2$ is not a two dimensional manifold.
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