Slightly darker patches appearing at the periphery of the iPad screen are usually attributable to one or more of the edge-lit backlight LEDs failing - or partial de-lamination of the backlight diffuser. The only remedy is full screen replacement.
Given that the screen backlighting and associated diffuser are integral elements of the iPad display - and that the screen is the single most expensive component of the iPad - replacement of the screen is unlikely to be economic. As such, assuming that the iPad is outside of the manufacturer's warranty, you might be best advised to live with the problem unless the issue makes the screen unusable.
You can check availability/eligibility of your iPad for repair - and associated cost for your country/region - here:
iPad Repair & Service - Apple Support