How can one deal with under-motivated students in the classroom?

This depends very much on the students and the classroom situation. Dealing with a six-year old who cannot sit still, a student turning in late assignments in a graduate seminar, or a high school student playing video games require quite different responses.

Unless you are teaching in an environment with very small class sizes and light teaching loads, the first step is acknowledging the limits of your own knowledge of your students. You might see behaviors such as late assignments, discipline issues, or attendance problems, but you don't necessarily know the reason behind them. A student whose parents are going through a messy divorce, a learning-disabled student, and a lazy student may all behave in similar ways. Quite often the issues behind student behaviors have little to do with you as a teacher or the class, but are grounded in the student's life situation. You cannot actually know whether lack of motivation or other issues underlie the behaviors you observe.

For some students, grades are a strong motivational factor and adhering to strict policies in attendance and grading can induce students to complete coursework. For students with learning disabilities or other mental or physical health issues, advisers or student health or counseling staff can help students in ways teachers cannot, and thus you should ensure that they get appropriate forms of help. A student with ADHD, for example, may appear unmotivated, but actually the lack of focus is due to a mental disability.

Although much ink has been expended on how to make coursework appear more relevant or how to "gamify" classes, there is a limit to teachers' responsibility. For very young students, trying to make the classroom more appealing through pedagogical techniques involving a highly interactive classroom may be effective, but for a university student taking a required class, especially a large lecture one, in which he or she has no interest at all, as long as the student is not disruptive, you should simply make the course requirements clear and focus your efforts on the more engaged students.