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Existence of solutions to second-order BVPs on time scales |
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| Authors: | Lynn Erbe Allan Peterson § Christopher C Tisdell ¶ |
| Institution: | 1. Department of Mathematics , University of Nebraska-Lincoln , Lincoln, NE 68588-0323, USA lerbe@math.unl.edu;3. Department of Mathematics , University of Nebraska-Lincoln , Lincoln, NE 68588-0323, USA;4. School of Mathematics , The University of New South Wales , Sydney NSW 2052, Australia |
| Abstract: | We consider a boundary value problem (BVP) for systems of second-order dynamic equations on time scales. Using methods involving dynamic inequalities, we formulate conditions under which all solutions to a certain family of systems of dynamic equations satisfy certain a priori bounds. These results are then applied to guarantee the existence of solutions to BVPs for systems of dynamic equations on time scales. |
| Keywords: | Boundary value problem System of equations Time scale Dynamic equation Existence of solutions AMS Subject Classifications: 39A10 39A99 |