What's going on with my cucumbers?

Factual Questions
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I’ve attempted a container garden this spring. Carrots are loving life. Bush beans are planning to take over the world. My cucumbers…are not doing so well. This is a bit of a surprise, as general consensus seems to be that the only things that will survive nuclear war are cockroaches, kudzu, and cucumber plants.

I have two varieties planted, Boston Pickling and Marketmore 76. The Marketmore’s have had a terrible germination rate anyway, but the Boston sprouts were doing quite well until about a week ago, when the edges of the leaves started curling, yellowing, and going brittle. The seed packet recommended that they get full sun, but we are in Arizona, so is there the possibility that they’re getting too much? I haven’t noticed any pests – save a lot of flies hanging around – but have been treating with an organic pesticide without any change. I’m using fertilizer stakes to keep them supplemented.

Pictures of the afflicted:

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Any ideas on where I’m going wrong?

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I believe I see a peat pot rim. I do don’t I? Rims of peat pots at the surface wick away water so that’s a bad thing. The soil doesn’t look like it has much humus and being Arizona I’d guess it’s highly alkaline and compact. You can have too much heat and sun which could be one of your problems. It’s really hard to tell at this stage of development. It also looks like you have fertilizer spread around the plants, which may be giving them a chemical burn. There are also many diseases that attack cucumbers. At this time you may wish to try planting some new seed directly into the soil. Use a good potting mix in the hole. the plants you have might do OK, but it only takes a couple weeks to get some new ones to that stage. You can always thin later if you need to. Always plant more seeds than you want plants and thin them as an insurance.