# I. V. Orlov

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### Elimination of Jacobi equation in extremal variational problems

Methods Funct. Anal. Topology **17** (2011), no. 4, 341-349

It is shown that the extremal problem for the one--dimensional Euler--Lagrange variational functional in ${C^1[a;b]}$ under a strengthened Legendre condition can be solved without using the Jacobi equation. In this case, exactly one of the two possible cases requires a restriction to the length of $[a;b]$, defined only by the form of the integrand. The result is extended to the case of compact extremum in ${H^1[a;b]}$.

### Strong compact properties of the mappings and K-Radon-Nikodym property

Methods Funct. Anal. Topology **16** (2010), no. 2, 183-196

For mappings acting from an interval into a locally convex space, we study properties of strong compact variation and strong compact absolute continuity connected with an expansion of the space into subspaces generated by the compact sets. A description of strong $K$-absolutely continuous mappings in terms of indefinite Bochner integral is obtained. A special class of the spaces having $K$-Radon-Nikodym property is obtained. A relation between the $K$-Radon-Nikodym property and the classical Radon-Nikodym property is considered.

### Compact variation, compact subdifferetiability and indefinite Bochner integral

Methods Funct. Anal. Topology **15** (2009), no. 1, 74-90

The notions of compact convex variation and compact convex subdifferential for the mappings from a segment into a locally convex space (LCS) are studied. In the case of an arbitrary complete LCS, each indefinite Bochner integral has compact variation and each strongly absolutely continuous and compact subdifferentiable a.e. mapping is an indefinite Bochner integral.

### Banach homomorphismtheorem in inductive scales of spaces and its applications

Methods Funct. Anal. Topology **10** (2004), no. 4, 74-85

### Iterated limit theorem for inductive-projective topologies and application

Methods Funct. Anal. Topology **10** (2004), no. 1, 54-62

### Normal functional indices and normal duality

Methods Funct. Anal. Topology **8** (2002), no. 3, 61-71