A few years ago I published a patent application, then gave up. Now with iPhone it maybe a good app. Do I stil have copyright?

A question without facts can't be answered. In general:

If your patent application was a utility application that was published by the Patent Office then the invention(s) claimed are now in the public domain. I don't know what you mean when you say that someone may write a software application for your invention. You need to speak with an intellectual property attorney to discuss what it is that you think you invented and potentially own.

If your application was not published then the claimed invention(s) may still be patentable (by the inventor) if all the patent prerequisites are met. If this is the case then you need to speak with a patent attorney about whether your "invention" is patentable -- or otherwise protectable via copyright or trade secret.

Good luck.

Thanks for your further explication of the question.

An invention can be "owned" as a bundle of rights contained in a patent, or in a copyright, or in a trade secret, or in knowhow or showhow.

Once a patent application is published, then what it discloses is no longer a secret. Once the application is abandoned without possibility of revival, consider the disclosure to be part of the "public domain." And it generally wouldn't qualify to be a "trade secret" in that situation.

I have already answered that yes, the author of the work probably owns a copyright in the code.

Does the inventor have the possibility of selling the idea to someone to turn it into an iPhone app? Probably, as knowhow or showhow, if the buyer is willing to receive such teaching from the inventor and pay something for it. That's typically an interesting opportunity for bargaining.

The answers above are correct. However, if you have a new and useful improvement to your invention that was not covered by the original patent application, you may be able to obtain patent protection for that new and useful improvement. Think of it this way, it appears the entirety of your original invention was put in the public domain when you abandoned the patent application (with no hope for revival). However, if you have subsequently added a feature to it, where that feature, by itself or in combination with what you originally described, is new and useful, then you may want to consider filing for a patent application on that feature and/or combination with your previous information.

This is all hypothetical, since you did not indicate you had an improvement - but it is something to think about.