No abstract

This paper is devoted to singular calculus of variations problems with constraints which are not regular mappings at the solution point, e.i. its derivatives are not surjective. We pursue an approach based on the constructions of the p-regularity theory. For p-regular calculus of variations problem we present necessary conditions for optimality in singular case and illustrate our results by classical example of calculus of variations problem.

The paper is devoted to the class of singular calculus of variations problems with constraints which are not regular mappings at the solution point. Methods of the p-regularity theory are used for investigation of isoperimetric and Lagrange singular problems. Necessary conditions for optimality in p-regular calculus of variations problem are presented.

In this paper we present a new solution method for underdetermined systems of nonlinear equations in a neighborhood of a certain point of the variety of solutions where the Jacoby matrix has incomplete rank. Such systems are usually called degenerate. It is known that the Gauss–Newton method can be used in the degenerate case. However, the variety of solutions in a neighborhood of the considered point can have several branches in the degenerate case. Therefore, the analysis of convergence of the method requires special techniques based on the constructions of the theory of p-regularity and p-factor-operators.