What is the meaning of persisting?

verb

• Continue to exist.
  • usage: "These stories die hard"; "The legend of Elvis endures"
  • synonyms: prevail, persist, die hard, run, endure
• Be persistent, refuse to stop.
  • usage: "he persisted to call me every night"; "The child persisted and kept asking questions"
  • synonyms: persevere, persist, hang in, hang on, hold on
• Stay behind.
  • usage: "The smell stayed in the room"; "The hostility remained long after they made up"
  • synonyms: persist, remain, stay

adjective

• Relentless and indefatigable in pursuit or as if in pursuit.
  • usage: "impossible to escape the dogging fears"
  • synonyms: dogging