Higher order nonlinear degenerate differential operator equations
type: Item
instance of: scholarly article
title: Higher order nonlinear degenerate differential operator equations
zbMATH Open document ID: 1183.47076
author: Donal O'Regan
author: Ravi P. Agarwal
author: Veli B. Shakhmurov
published in: Applied Mathematics Letters
publication date: 2009-10-14T00:00:00Z
review text: The authors present optimal regularity results in \(L^p(0,a;E)\) for nonlocal boundary value problems for higher order nonlinear degenerate differential operator equations of the type \[ (-1)^m u^{[2m]}(x) +\sum_{i=0}^{2m-1} A_i(x) u^{[i]}(x)+Au(x)=F(x,u, u^{[1]},\dots,u^{[2m-1]}) \] with boundary conditions \[ \sum_{i=0}^{m_k}\alpha_{ki}u^{[i]}(0) +\beta_{ki}u^{[i]}(a)=0,\quad k=1,2,\dots,2m. \] Here, \(u^{[i]}=\left(x^\gamma {d\over {dx}}\right)^i u,\) \(0<\gamma<1-1/p,\) \(0\leq m_k\leq 2m-1,\) \(\alpha_{ki}\) and \(\beta_{ki}\) are complex numbers, while \(A_i\) and \(A\) are possibly linear operators in a Banach space \(E\).
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34G20
Mathematics Subject Classification ID: 35R20
Mathematics Subject Classification ID: 35J70
zbMATH DE Number: 5615123
zbMATH Keywords: operator-valued multipliers
zbMATH Keywords: interpolation of Banach spaces
zbMATH Keywords: boundary value problems
zbMATH Keywords: differential operator equations
zbMATH Keywords: abstract nonlinear equations
reviewed by: Dian K. Palagachev
MaRDI profile type: Publication
full work available at URL: j.aml.2009.04.004
OpenAlex ID: W2040027589
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DOI: 10.1016/J.AML.2009.04.004
description: scientific article; zbMATH DE number 5615123