@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} } @article{MkrtchianHenkel2020, author = {Mkrtchian, Vanik E. and Henkel, Carsten}, title = {Green function solution of generalised boundary value problems}, series = {Physics Letters A}, volume = {384}, journal = {Physics Letters A}, number = {23}, publisher = {Elsevier}, address = {Amsterdam}, issn = {0375-9601}, doi = {10.1016/j.physleta.2020.126573}, pages = {5}, year = {2020}, abstract = {We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the boundary value problem of an inhomogeneous partial differential equation with inhomogeneous, nonlocal boundary conditions. The construction applies for a broad class of linear partial differential equations and linear boundary conditions.}, language = {en} }