Abstract A variational principle is established by the semi-inverse method and used to solve approximately a nonlinear problem Ritz method. In this process,it may be difficult large system of algebraic equations,the Groebner bases theory (Buchberger’s algorithm) applied problem. The results show that approach much simpler more efficient.

Parametric and nonparametric necessary and sufficient optimality conditions are established for a class of nonconvex variational problems with generalized fractional objective functions and nonlinear inequality constraints containing arbitrary norms. Based on these optimality criteria, ten parametric and parameterfree dual problems are constructed and appropriate duality theorems are proved. Th...