有着 / V + 有: to possess (formal), to bear (inscribed or attached)
【五38】“有”字句 / special sentence patterns
Tone colorsā tone 1á tone 2ǎ tone 3à tone 4a neutral
有着 is the formal "to have" for weighty or abstract things: a history, a role, an influence, relations (这座城市有着两千多年的历史). The 着 here is a fixed ending: it does not mean "in progress". You also find it before a descriptive feature (有着一双大眼睛).
Place / thing + V + 有 + object describes what is written, carved, hung or contained somewhere: 书上写有他的名字, 门上刻有一朵花, 盒子里装有几十张老照片. The verb (写、刻、挂、画、印、装) says how the thing is carried, and 有 presents the object as new information. This is the style of labels, captions and museum texts; after 有 you never add 了, 过 or 着.
For an ordinary "to have" keep 有 (我有一个哥哥). To say where something is, V + 着 (墙上挂着一幅画) is the most natural in speech; V + 有 says the same thing in a more written, more informative way. Never stack 有 and 着 after the verb.
Examples
书上写有他的名字。
Shū shang xiě yǒu tā de míngzi.His name is written in the book.
门上刻有一朵花。
Mén shang kè yǒu yì duǒ huā.A flower is carved on the door.
这个孩子有着一双明亮的大眼睛。
Zhège háizi yǒuzhe yì shuāng míngliàng de dà yǎnjing.This child has a pair of bright, big eyes.
这座城市有着两千多年的历史。
Zhè zuò chéngshì yǒuzhe liǎng qiān duō nián de lìshǐ.This city has more than two thousand years of history.
盒子里装有几十张老照片，每一张后面都写有日期。
Hézi li zhuāng yǒu jǐ shí zhāng lǎo zhàopiàn, měi yì zhāng hòumiàn dōu xiě yǒu rìqī.The box holds dozens of old photos, and each one has a date written on the back.
两国之间有着长期的友好关系。
Liǎng guó zhījiān yǒuzhe chángqī de yǒuhǎo guānxì.The two countries have long-standing friendly relations.
Common mistakes
✗ 我有着一个哥哥 → ✓ 我有一个哥哥 (有着 is for abstract objects or characteristic features, not for a plain "I have a brother").
✗ 墙上挂有着一幅画 → ✓ 墙上挂有一幅画 / 墙上挂着一幅画 (do not stack 有 and 着).
✗ 书上写有了他的名字 → ✓ 书上写有他的名字 (V + 有 describes a state: no 了).