Answer: TIlling will bring more weed seeds to the surface where they will germinate, so it won't really solve the problem. If the weed are annual weeds such as crabgrass you can stop them by mulching next spring. If they are perennial weeds such as dandelions you may be able to smother them with newspaper and a heavy mulch or you may want to spot treat them with a herbicide such as glyphosate. Keep in mind that newspaper and a mulchheavy enough to hinder perennial weeds may hinder your bulbs, so it would probably be better to apply it in spring after the bulbs are up so you can see where they are. Be sure, though to do it early enough before the warm season weeds germinate again. Keep in mind too that the weeds are always the worst the first year and decrease after that.
Edging needs to be continuous and needs to be buried in the soil to keep spreading grasses out. Another option is to keep a band of soil that is covered in newspaper and mulch between the lawn and the garden, or to periodically spray a bordering band with an herbicide. Further options are to hand dig a sharp edge or to use raised beds.
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