@article{AlsaedyTarkhanov2014,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  series = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  volume    = {95},
  journal   = {Nonlinear analysis : theory, methods \& applications ; an international multidisciplinary journal},
  publisher = {Elsevier},
  address   = {Oxford},
  issn      = {0362-546X},
  doi       = {10.1016/j.na.2013.09.024},
  pages     = {468 -- 482},
  year      = {2014},
  abstract  = {We investigate nonlinear problems which appear as Euler-Lagrange equations for a variational problem. They include in particular variational boundary value problems for nonlinear elliptic equations studied by F. Browder in the 1960s. We establish a solvability criterion of such problems and elaborate an efficient orthogonal projection method for constructing approximate solutions.},
  language  = {en}
}
@unpublished{AlsaedyTarkhanov2013,
  author    = {Alsaedy, Ammar and Tarkhanov, Nikolai Nikolaevich},
  title     = {Normally solvable nonlinear boundary value problems},
  issn      = {2193-6943},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus-65077},
  year      = {2013},
  abstract  = {We study a boundary value problem for an overdetermined elliptic system of nonlinear first order differential equations with linear boundary operators. Such a problem is solvable for a small set of data, and so we pass to its variational formulation which consists in minimising the discrepancy. The Euler-Lagrange equations for the variational problem are far-reaching analogues of the classical Laplace equation. Within the framework of Euler-Lagrange equations we specify an operator on the boundary whose zero set consists precisely of those boundary data for which the initial problem is solvable. The construction of such operator has much in common with that of the familiar Dirichlet to Neumann operator. In the case of linear problems we establish complete results.},
  language  = {en}
}