The fourth son of Antiochus VIII was supported by Ptolemy VII in challenging his brother Philip I & cousin Antiochus X for control of Syria (92 BCE). Having occupied Damascus, Demetrius claimed all southern Syria including Palestine. After Antiochus X died, he & Philip divided Syria between them. When Greek cities of the Decapolis appealed for aid in warding off the expansionist policies of the Hasmonean dynasty, Demetrius sent an army that dealt the Judean ruler, Alexander Jannai, a devastating defeat at Shechem (89 BCE). Emboldened by this triumph, he turned his army to challenge his brother Philip for sole control of the Seleucid empire.  But Philip, aided by the Parthians defeated, captured & exiled him (87 BCE). He died a few years later, a royal hostage in Parthia. 

References: Josephus, Antiquities 13.370-386.

Other resources on line:

• Demetrius III Eucaerus - Jona Lendering outlines key events & lists primary sources [Livius: Articles in Ancient History].

• Demetrius III Eucaerus - brief article in Wikipedia's growing web.

This silver tetradrachma minted by Demetrius III in 90 BCE illustrates the exaggerated pretensions of the royal cult in the late Seleucid empire. The face bears a realistic likeness of a monarch who died in captivity without heirs less than half a decade later, while the inscription on the reverse [surrounding a cultic statue of the Syrian fertility goddess, Atargatis] proclaims his divinity in terms suggesting triumphant immortality: Basileos Demetriou Theou Philopatros Soteros ["of King Demetrius: God, Fatherloving Savior"].