Positive Radial Solutions to the Double Singular $k_i$-Hessian System: Existence, Multiplicity and Dependence on a Parameter

Abstract

In this paper, the author is concerned with the positive radial solutions for a double singular $k_i$-Hessian system with a parameter $\lambda $. We establish a criterion on the existence of a positive radial solution for small $\lambda $, a criterion on the multiplicity of positive radial solutions for certain ranges of $\lambda $, and a criterion on the nonexistence of positive radial solutions in the case $\lambda \gg 1$. The dependence of the positive radial solution on the parameter $\lambda $ is also studied.

Keywords

Singular $k_i$-Hessian system / Cone and partial ordering / Contradiction argument / Positive solutions / Existence / Nonexistence and multiplicity / 35J57 / 35J96

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Funding

Natural Science Foundation of Beijing Municipality(1212003)

Rights & permissions

School of Mathematical Sciences, University of Science and Technology of China and Springer-Verlag GmbH Germany, part of Springer Nature