Assuming your desktop applications does not use any open source projects other than PostgreSQL, you are not required to release the source code of your desktop application. However, you are required to provide the following text along with your Desktop application.
Portions Copyright (c) 1996-2017, The PostgreSQL Global Development
Portions Copyright (c) 1994, The Regents of the University of
Permission to use, copy, modify, and distribute this software and its
documentation for any purpose, without fee, and without a written
agreement is hereby granted, provided that the above copyright notice
and this paragraph and the following two paragraphs appear in all
IN NO EVENT SHALL THE UNIVERSITY OF CALIFORNIA BE LIABLE TO ANY PARTY
FOR DIRECT, INDIRECT, SPECIAL, INCIDENTAL, OR CONSEQUENTIAL DAMAGES,
INCLUDING LOST PROFITS, ARISING OUT OF THE USE OF THIS SOFTWARE AND
ITS DOCUMENTATION, EVEN IF THE UNIVERSITY OF CALIFORNIA HAS BEEN
ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
THE UNIVERSITY OF CALIFORNIA SPECIFICALLY DISCLAIMS ANY WARRANTIES,
INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF
MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE. THE SOFTWARE
PROVIDED HEREUNDER IS ON AN "AS IS" BASIS, AND THE UNIVERSITY OF
CALIFORNIA HAS NO OBLIGATIONS TO PROVIDE MAINTENANCE, SUPPORT,
UPDATES, ENHANCEMENTS, OR MODIFICATIONS.
Edit: If your desktop application doesn't include any PostgreSQL software (i.e. all PostgreSQL software is on the server side), then you are not required to give attribution or licensing information. It might be polite to mention your server is using it, but it is definitely not required in this scenario.