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Euler-lagrange Equation for a Delay Variational Problem

Jafar Lavasani, Zeinab | 2017

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  1. Type of Document: M.Sc. Thesis
  2. Language: Farsi
  3. Document No: 49879 (02)
  4. University: Sharif University of Technology
  5. Department: Mathematical Sciences
  6. Advisor(s): Hesaraki, Mahmoud
  7. Abstract:
  8. In the first chapter of this thesis we consider the simplest problem of calculus of variation with mixed boundary conditions and we obtain the Euler-Lagrange equation. We will see that the work here is very similar to the work for Dirichlet boundary conditions. In chapter two we investigate the sufficient condition for the existence of solution. Here we will see the work is really different from the work for Dirichlet condition. In fact this result is published in a credible journal. The main work of this thesis will begin in chapter three and will end in chapter five. In these chapters we will investigate a necessary condition for existence of solution for a calculus of variation problem which has a delay term in the integrand for the unknown function and we obtain an Euler-Lagrange equation for this problem. In fact if we compare with the result for the simplest problem, we should say that here we obtain a delay differential equation of second order instead of a second order ordinary differential equation. Here we should mention that for this investigation we take advantage of some advanced facts from functional analysis. Finally, we must say that the sufficient condition for existence of solution is not trivial. In fact some advanced and new tools must be made
  9. Keywords:
  10. Eulerian-Lagrangian Equation ; Delay Differential Equations ; Dirichelt Boundary Condition ; Nemytskii Operator ; Sufficient Jacobi Condition

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