Second order iterative dynamic boundary value problems with mixed derivative operators with applications. (English) Zbl 1512.34153
Summary: In this paper, we derive sufficient conditions for the existence and uniqueness of solutions of the iterative dynamic boundary value problem of second order with mixed derivative operators. For the existence, we utilize Schauder’s fixed point theorem while for uniqueness we apply contraction mapping principle. Further, a continuous dependence of bounded solutions to the addressed problem is studied. Finally, we demonstrate the validity of our findings by constructing examples as applications to beam deflection due to thermal stress and temperature distribution along the wire.
MSC:
| 34K42 | Functional-differential equations on time scales or measure chains |
| 34K43 | Functional-differential equations with state-dependent arguments |
| 34K10 | Boundary value problems for functional-differential equations |
| 47N20 | Applications of operator theory to differential and integral equations |
Keywords:
iterative differential equation; functional boundary value problem; time scale; mixed derivativesReferences:
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