Literary or poetic term for the setting sun, often evoking a sense of decline or the end of an era.
The setting sun sinks behind the mountains.
noun, noun which may take the genitive case particle 'no'
Figurative use for the decline of an industry, institution, or way of life; often used with 産業, 時代, etc.
Even in industries called declining, they can be revived with new technology.
This shipbuilding industry, too, is now in decline.
The mountains are beautifully bathed in the light of the setting sun.
The town's economy is steadily declining.
衰退 is a general, neutral term for decline used in many contexts, while 斜陽 evokes the poetic image of a setting sun to describe the decline of an industry or era.
没落 emphasizes a fall from a formerly prosperous or high status, whereas 斜陽 focuses on a gradual, ongoing waning.
From 斜 (しゃ, 'slanting') + 陽 (よう, 'sun, sunlight'), literally 'slanting sun', referring to the sun low in the sky at sunset. The figurative sense of decline comes from the image of the sun going down.