### Variational and boundary value problems with perturbations

#### Abstract

In the paper an optimization problem with parameters is considered. Some

sufficient conditions under which the solutions of the problem continuosly

depend on parameters (in the weak or the strong topology of a Banach space)

are proved. Moreover, some applications to the eigenvalue and boundary value

problems for differential operators are given.

sufficient conditions under which the solutions of the problem continuosly

depend on parameters (in the weak or the strong topology of a Banach space)

are proved. Moreover, some applications to the eigenvalue and boundary value

problems for differential operators are given.

#### Keywords

Optimization problem; stability analysis; eigenvalue problem; boundary value problem

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