Linear and nonlinear abstract differential equations of high order

Veli B. Shakhmurov

Open Mathematics (2015)

  • Volume: 13, Issue: 1, page 2383-2397
  • ISSN: 2391-5455

Abstract

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The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.

How to cite

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Veli B. Shakhmurov. "Linear and nonlinear abstract differential equations of high order." Open Mathematics 13.1 (2015): 2383-2397. <http://eudml.org/doc/271775>.

@article{VeliB2015,
abstract = {The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.},
author = {Veli B. Shakhmurov},
journal = {Open Mathematics},
keywords = {Differential equations; Semigroups of operators; Abstract function spaces; Nonlocal boundary value problems; Spectral properties of differential operators; abstract boundary value problems; nonlocal conditions; equations with parameter},
language = {eng},
number = {1},
pages = {2383-2397},
title = {Linear and nonlinear abstract differential equations of high order},
url = {http://eudml.org/doc/271775},
volume = {13},
year = {2015},
}

TY - JOUR
AU - Veli B. Shakhmurov
TI - Linear and nonlinear abstract differential equations of high order
JO - Open Mathematics
PY - 2015
VL - 13
IS - 1
SP - 2383
EP - 2397
AB - The nonlocal boundary value problems for linear and nonlinear degenerate abstract differential equations of arbitrary order are studied. The equations have the variable coefficients and small parameters in principal part. The separability properties for linear problem, sharp coercive estimates for resolvent, discreetness of spectrum and completeness of root elements of the corresponding differential operator are obtained. Moreover, optimal regularity properties for nonlinear problem is established. In application, the separability and spectral properties of nonlocal boundary value problem for the system of degenerate differential equations of infinite order is derived.
LA - eng
KW - Differential equations; Semigroups of operators; Abstract function spaces; Nonlocal boundary value problems; Spectral properties of differential operators; abstract boundary value problems; nonlocal conditions; equations with parameter
UR - http://eudml.org/doc/271775
ER -

References

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