Variational problem for functionals containing deviating parameters (Q2719442)

Let \( G\subset \mathbb{R}^2 \) be a bounded domain of arbitrary shape. In the paper are discussed variational problems for functionals of the form NEWLINE\[NEWLINEJ(x) = \int_G F(t,s,x(t,s-1),x(t,s),x(t,s+1), \quad x_t',(t,s-1),x_t'(t,s),x_t'(t,s+1)) dt ds\tag{1} NEWLINE\]NEWLINE under certain boundary conditions. Necessary conditions are established for extrema of the functionals. Examples of boundary value problems are considered for differential-difference equations.