I would like to know if it is possible to make an application to be sold on Apple AppStores that is linked (during compilation) to a BSD-licensed library.
In theory it should be fine.
The BSD license is a Permissive free software license which means it doesn't insist on anything using it being shared in the same way.
The BSD license only says that redistribution and use in source and binary forms are permitted (subject to certain constraints) but doesn't mandate how that should be other than that the copyright notices should remain intact if it is.
You have several versions of the BSD license. It's one of the simplest licenses, so you should simply read it.
Here is the "longest one":
Redistribution and use in source and binary forms, with or without modification, are permitted provided that the following conditions are met:
- Redistributions of source code must retain the above copyright notice, this list of conditions and the following disclaimer.
- Redistributions in binary form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
- All advertising materials mentioning features or use of this software must display the following acknowledgement: This product includes software developed by the .
- Neither the name of the nor the names of its contributors may be used to endorse or promote products derived from this software without specific prior written permission.
So, yes, you can redistribute it on app stores. Just include the copyright in your distribution.