Growth of solutions for measure differential equations and dynamic equations on time scales

Abstract

In this paper, we investigate the asymptotic behavior for measure differential equations and dynamic equations on time scales via generalized ordinary differential equations (generalized ODEs, for short). At first, we establish new results that guarantee the existence of unbounded solutions for generalized ODEs, and after that, using the known correspondence between generalized ODEs and measure differential equations, also between measure differential equations and dynamic equations on time scales, we obtain similar results for these equations. Finally, we present an application to illustrate our main results.