Answer: Unfortunately growing perennials near a black walnut can be quite difficult. The walnut tree's roots will likely extend well beyond the branch spread of the tree, stealing moisture and nutrients from your plants, as well as carrying the toxic juglone. I have found that violets and daffodils grow quite well under black walnuts, as do phlox.
Here are links to several articles about gardening near black walnut trees that you may find interesting; these also include lists of suggested and non-recommended plants.
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