Positive solutions of the singular semipositone boundary value problem on time scales

By constructing a special cone and using the spectrum theory of a bounded positive operator and fixed point index theory, this paper deals with the existence of positive solutions for the singular semipositone boundary value problem on time scales, and thus improves and generalizes the results of related papers. Emphasis is put on the fact that the nonlinear term f may take a negative value. An example is also included to illustrate the importance of the results obtained.