Bifurcation analysis for nonlinear elliptic boundary value problems with combined nonlinearity of absorption and blowing up effects arising in population dynamics

在本研究中，我们利用分歧分析的方法，考虑了一类具有非线性边界条件的非线性椭圆型种群动力学问题正解的存在性。非线性表现为Logistic非线性和幂次非线性的结合，幂次非线性是指种群在边界上的输入通量。通过参数的取值，我们确定了正解分支分量的全局性态，并由此讨论了在一定参数范围内正解的唯一性和多解性.不确定性系数的空间异质性对该问题的解决起着重要的作用。

In this study, we consider the existence of positive solutions of nonlinear elliptic problems with nonlinear boundary conditions arising in population dynamics, by means of bifurcation analysis. The nonlinearity shows logistic nonlinearity combined with the power nonlinearity which means the incoming flux of population on the boundary. We determine the global behavior of bifurcation components of the positive solutions according to values of a parameter, and by this, we can also discuss the uniqueness and multiplicity of the positive solutions in some range of the parameter. The spatial heterogeneity of the indefinite coefficient equipped with the problem plays an important role.