Abstract We study the one-dimensional diffusive generalized logistic problem with constant yield harvesting: { u ″ ( x ) + λ g ( u ) − μ = 0 , − 1 x 1 , u ( − 1 ) = u ( 1 ) = 0 , where λ , μ > 0 . We assume that nonlinearity g satisfies g ( 0 ) = g ( 1 ) = 0 , g ( u ) > 0 on ( 0 , 1 ) , and g either is concave on ( 0 , 1 ) or (is concave-convex on ( 0 , 1 ) and satisfies a certain condition). We prove that, for any fixed μ > 0 , on the ( λ , ‖ u ‖ ∞ ) -plane, the bifurcation diagram consists of a ⊂-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying μ > 0 . We also prove that, for any fixed λ > π 2 4 g ′ ( 0 ) , on the ( μ , ‖ u ‖ ∞ ) -plane, the bifurcation diagram consists of a reversed ⊂-shaped curve and then we study the structures and evolution of bifurcation diagrams for varying λ > π 2 4 g ′ ( 0 ) .

中文翻译：

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具有恒定产量收获的一维扩散广义逻辑问题的分叉图的结构和演化

摘要 我们研究了具有恒定产量收获的一维扩散广义逻辑问题：{ u ″ ( x ) + λ g ( u ) − μ = 0 , − 1 x 1 , u ( − 1 ) = u ( 1 ) = 0 , 其中 λ , μ > 0 。我们假设非线性 g 满足 g ( 0 ) = g ( 1 ) = 0 ， g ( u ) > 0 在 ( 0 , 1 ) 上，并且 g 在 ( 0 , 1 ) 上是凹面或在 ( 是凹凸0 , 1 ) 并满足一定条件)。我们证明，对于任何固定的 μ > 0 ，在 ( λ , ‖ u ‖ ∞ ) 平面上，分叉图由⊂形曲线组成，然后我们研究了不同 μ > 0 时分叉图的结构和演化. 我们还证明，对于任何固定的 λ > π 2 4 g ′ ( 0 ) ，在 ( μ , ‖ u ‖ ∞ ) 平面上，