Application of Green ’ S Operator to Quadratic Variational Problems

  title={Application of Green ’ S Operator to Quadratic Variational Problems},
  author={Nikolay V. Azbelev and Vadim Z. Tsalyuk},
  • Nikolay V. Azbelev, Vadim Z. Tsalyuk
  • Published 2005
We use Green’s function of a suitable boundary value problem to convert the variational problem with quadratic functional and linear constraints to the equivalent unconstrained extremal problem in some subspace of the space L2 of quadratically summable functions. We get the neccessary and sufficient criterion for unique solvability of the variational problem in terms of the spectrum of some integral Hilbert–Schmidt operator in L2 with symmetric kernel. The numerical technique is proposed to… CONTINUE READING