Yeah, University of Kansas does provide scholarships based on merit. Here are some of them:

KU Excellence
Total Worth: $16,210/yr
Eligibility: $16,210/yr
Minimum Criteria: 30 ACT or 1360 SAT + 3.75 GPA
Separate application needed: No

KU Distinction
Total Worth: $13,687/yr
Eligibility: $13,687/yr
Minimum Criteria: 28 ACT or 1300 SAT + 3.5 GPA
Separate application needed: No

Chancellor
Total Worth: $5,000/yr
Eligibility: $5,000/yr
Minimum Criteria: 32 ACT or 1420 SAT + 3.85 GPA
Separate application needed: No

University of Kansas provides aids at an average of 16455 per student meeting 79% of students need. 98% of students with need receive financial aid at an average of 8743 need-based grant. They also provide other scholarships including Kansas Ethnic Minority Scholarship and Pepsi Scholarship.