Answer: Walnut trees contain a growth inhibiting chemical called juglone. All parts of the tree, including roots, bark, leaves and fruit release this chemical. (It's a defense mechanism to prevent competition by keeping other plants from encroaching on the walnut trees.) Some plants are more tolerant of juglone and will grow within a reasonable distance of the trees, but other plants are highly sensitive and will exhibit symptoms of yellowing and wilting foliage, and eventual death. Tomatoes are highly susceptible to juglone.
Another consideration in gardening close to stands of large trees is that trees have large root systems with many surface (or feeder) roots. It's likely that the roots from these trees are taking the moisture and nutrients from the soil, leaving your tomato plants with less than needed to sustain life. By virtue of their size and appetites, trees generally win the competition for moisture and nutrients.
You might want to move your garden to a location far from the trees. Failing that, try gardening in raised beds (with a weed barrier placed over the surface of the soil before filling the bed with topsoil to keep roots at bay), or plant your tomatoes in containers, placing them on a sunny deck or patio.
Q&A Library Searching Tips