MacBook Air black screen on LG external display

Hello Apple Community,

I have a problem with my MacBook Air and LG display.

Is a 13-inch MacBook Air (Early 2014), 1,4 GHz Intel Core i5 processor, 4 GB 1600 MHz DDR3 memory, Intel HD Graphics 5000 1536 MB with installed macOS Mojave (10.14.1 [18B75]);

The monitor is a LG HDR WFHD 34WK650 ultra wide external display (34-inch) connected via Mini-DisplayPort/Thunderbolt 2 (Mac) to DisplayPort (display).

When I connect the monitor to the Mac via DisplayPort cable, the Mac recognizes the monitor resolution (2560 x 1080) and I can interract with the secondary desktop, but the external display doesn't show any image (always black screen).

The monitor is correctly connected to the power with his in-box cable and is powered on, with the DisplayPort port as image input.

If I connect the Mac to the monitor via HDMI cable (connected to the Mac with an adaptor), the monitor starts showing the secondary desktop but with a 1080p resolution, showing a distorted image to fill the entire screen of 2560 x 1080 pixels.

I tried to fix this problem with some third-party apps [Dual Controller (official LG app) and OnScreen Control (official LG app) both downloaded form the official LG website, and SwitchResX] but it doesn't work.

I temporarily fixed the problem by installing an older version of macOS (Mac OS X Mavericks), and the monitor works correctly.

The external display works correctly also with my Mac mini (Mid 2011) with installed macOS High Sierra (10.13.6 [17G3025]), connected via Mini-DisplayPort to DisplayPort cable.

Is a Mac mini (Mid 2011), 2,3 GHz Intel Core i5 processor, 5 GB 1333 MHz DDR3 memory, Intel HD Graphics 3000 384 MB.

The question is:

How I can use my MacBook Air without installing an older version of macOS but keeping macOS Mojave 10.14.1?

Thanks in advance for your help!