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arXiv · 1205.3848

Nonlinear elliptic equations with a singular perturbation on compact Lie groups and Homogeneous spaces

Weiping Yan·Yong Li
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Abstract

This paper is devoted to the study of a class of singular perturbation elliptic type problems on compact Lie groups or homogeneous spaces $\mathcal{M}$. By constructing a suitable Nash-Moser-type iteration scheme on compact Lie groups and homogeneous spaces, we overcome the clusters of "small divisor" problem, then the existence of solutions for nonlinear elliptic equations with a singular perturbation is established. Especially, if $\mathcal{M}$ is the standard torus $\textbf{T}^n$ or the spheres $\textbf{S}^n$, our result shows that there is a local uniqueness of spatially periodic solutions for nonlinear elliptic equations with a singular perturbation.

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Weiping Yan, Yong Li. 2012-05-17. Nonlinear elliptic equations with a singular perturbation on compact Lie groups and Homogeneous spaces. https://arxiv.org/abs/1205.3848

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