This is a Phase II study design, premature infants (inpatient in neonatal intensive care units) will be randomized in a dose escalating approach 3:1 (sildenafil: placebo) into 3 cohorts with escalating doses of sildenafil. There will be 40 randomized and dosed participants in each cohort for a total of up to 120 participants. Cohort 1 sildenafil dose will be 0.125 mg/kg q 8 hours IV or 0.25 mg/kg q 8 hours enteral. Cohort 2 sildenafil dose will be 0.5 mg/kg q 8 hours IV or 1.0 mg/kg q 8 hours enteral. Cohort 3 sildenafil dose will be 1 mg/kg q 8 hours IV or 2 mg/kg q 8 hours enteral.