Abstract This article ascertains the global structure of the diagram of positive solutions of a very general class of elliptic boundary value problems with spatial heterogeneities and nonlinear mixed boundary conditions, considering as bifurcation-continuation parameter a certain parameter γ that appears in the boundary conditions. In particular, in this work are obtained, in terms of such a parameter γ, the exact decay rate to zero and blow-up rate to infinity of the continuum of positive solutions of the problem, at the bifurcations from the trivial branch and from infinity. The new findings of this work complement, in some sense, those previously obtained for Robin linear boundary conditions by J. García-Melián, J. D. Rossi and J. C. Sabina de Lis in 2007. The main technical tools used to develop the mathematical analysis carried out in this paper are local and global bifurcation, continuation, comparison and monotonicity techniques and blow-up arguments.

中文翻译：

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非线性混合边界条件下具有分岔-连续参数的异构椭圆 BVP

摘要 本文确定了一类具有空间异质性和非线性混合边界条件的非常一般的椭圆边值问题的正解图的全局结构，将边界条件中出现的某个参数γ作为分岔-连续参数。特别地，在这项工作中，根据这样的参数 γ，在从平凡分支和从无穷大的分岔处，问题的正解的连续统的精确衰减率为零和爆破率到无穷大. 在某种意义上，这项工作的新发现补充了 J. García-Melián、J. D. Rossi 和 J. C. Sabina de Lis 于 2007 年针对 Robin 线性边界条件获得的结果。