Browsing by Author "Agarwal, Ravi P."

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Citation Count: 0
Higher order nonlinear degenerate differential operator equations
(Pergamon-elsevier Science Ltd, 2009) Agarwal, Ravi P.; O'Regan, Donal; Shakhmurov, Veli
In this work we present optimal regularity results for nonlocal boundary value problems for higher order nonlinear degenerate differential operator equations. Solutions will be sought in the space W-p,gamma([2m]). (C) 2009 Elsevier Ltd. All rights reserved.
Citation Count: 3
B-Separable boundary value problems in Banach-valued function spaces
(Elsevier Science inc, 2009) Agarwal, Ravi P.; O'Regan, Donal; Shakhmurov, Veli B.
In this paper, the nonlocal boundary value problems for anisotropic partial differential-operator equations with dependent coefficients in Banach-valued Besov (B) spaces are studied. The principal parts of the appropriate differential operators are non-self-adjoint. Several conditions for separability and Fredholmness are given. These results permit us to establish that the inverse of the corresponding differential operators belong to the Schatten q-class. The spectral properties of the appropriate differential operators are also investigated. In addition we study the maximal regularity of nonlocal initial boundary value problems for abstract parabolic equations, finite or infinite systems of parabolic equations and the separability of nonlocal boundary value problems for finite or infinite systems of quasi-elliptic equations in B spaces. (C) 2008 Elsevier Inc. All rights reserved.
Citation Count: 1
Linear and nonlinear degenerate boundary value problems in Besov spaces
(Pergamon-elsevier Science Ltd, 2009) Shakhmurov, Veli B.; Agarwal, Ravi P.
The boundary value problems for linear and nonlinear degenerate differential-operator equations in Banach-valued Besov spaces are studied. Several conditions for the separability of linear elliptic problems are given. Moreover, the positivity and the analytic semigroup properties of associated differential operators are obtained. By using these results, the maximal regularity of degenerate boundary value problems for nonlinear differential-operator equations is derived. As applications, boundary value problems for infinite systems of degenerate equations in Besov spaces are studied. Published by Elsevier Ltd
Citation Count: 4
Uniform separable differential operators with parameters
(Pergamon-elsevier Science Ltd, 2010) Agarwal, Ravi P.; O'Regan, Donal; Shakhmurov, Veli B.
In this paper we study boundary value problems for anisotropic partial differential-operator equations with parameters. The principal part of the appropriate differential operators are not self-adjoint. Several conditions for the uniform separability in weighted Banach-valued L-p-spaces are given. Sharp estimates for the resolvent of the corresponding differential operator are obtained. In particular the positivity and R-positivity of these operators are established. As an application we study the separability of degenerate DOEs, maximal regularity for degenerate abstract parabolic problem with parameters, the uniform separability of finite and infinite systems for degenerate anisotropic partial differential equations with parameters. (c) 2009 The Franklin Institute. Published by Elsevier Ltd. All rights reserved.