(It should be noted that in Islam the night of Monday is Sunday night).
According to a traditional report, transmitted on the authority of al-A'mash, Anas ibn Malik (may Allah be well pleased with him) stated that Allah's Messenger (Allah bless him and give him peace) once said:
If someone performs four [voluntary] cycles of ritual prayer [raka'at] on a Monday night-reciting in the first cycle "Al-hamdu li'llahi... [Praise be to Allah...']" one time, and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" ten times, and in the second cycle "Al-hamdu li'llahi... [Praise be to Allah...']" one time, and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" twenty times, and in the third cycle "Al-hamdu li'llahi... [Praise be to Allah...']" one time, and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" thirty times, and in the fourth cycle "Al-hamdu li'llahi... [Praise be to Allah...']" one time, and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" forty times--and if he then pronounces the testimony and the salutation [tashahhada wa sallama], and recites "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" seventy-five times, and begs forgiveness of Allah for himself and his parents seventy-five times, and invokes Allah's blessing on the Prophet (Allah bless him and give him peace) seventy-five times, and then asks [in his supplication] for his need to be satisfied--it will be an obligation [haqq] incumbent upon Allah (Exalted is He) to satisfy his need.
This is actually called the Ritual Prayer of Need [salat al-haja].
According to another traditional report, this transmitted on the authority of Abu Umama (may Allah be well pleased with him), Allah's Messenger (Allah bless him and give him peace) once said:
If someone performs two [voluntary] cycles of ritual prayer [rak'atain] on a Monday night-reciting in the each cycle the Opening Sura of the Book [Fatihat al-Kitab] one time, and "Qul Huwa'llahu Ahad [Say: 'He is Allah, One!']" fifteen times--and if he recites the Verse of the Throne [Ayat al-Kursi] fifteen times after the salutation [taslim], and begs forgiveness of Allah (Glorified and Exalted is He) fifteen times--Allah (Exalted is He) will include his name among the names of those who belong to the Garden of Paradise, even if he is one of those who [would otherwise] belong to the Fire of Hell, and He will forgive him his sins of flagrant wrongdoing. For every Qur'anic verse [aya] he recites, He will credit him with a Pilgrimage [Hijja] and a Visitation ['Umra], and if he dies between that Monday and the next Monday, he will die as a martyr [shahid].
