On boundary value problems for a class of functional-differential equations
type: Item
instance of: scholarly article
title: On boundary value problems for a class of functional-differential equations
zbMATH Open document ID: 1017.34069
DOI: 10.1016/S0362-546X(01)00141-9
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-06-27T00:00:00Z
review text: Let \(q> 1\) and \(f\in L_2(0,T)\) be a complex-valued function. The author considers the functional-differential equations \[ -\Biggl(\sum^{N_1}_{m= -N_2} a_m u'(q^{-m}t)\Biggr)= f(t),\tag{1} \] where \(a_m\in \mathbb{C}\), \(N_2> 0\), \(a_{N_1}, a_{N_2}\neq 0\) and \[ -\Biggl(\sum^l_{m=0} b_m(t) u'(q^{-m}t)\Biggr)'+ (A_1u)(t)= f(t),\tag{2} \] where \(b_m\in C^1[0,T]\) are complex-valued functions and \(A_1: AC^1(J)\to L_2(0,T)\) is a linear bounded operator together with the homogeneous boundary conditions \[ u(t)= 0\quad\text{for }t\not\in (0,T)\tag{3} \] and \[ u(0)= u(T)= 0.\tag{4} \] The paper presents conditions for the solvability of BVPs (1), (3) and (2), (4) in the class \(AC^1[0,T]\) (functions having absolutely continuous derivatives on \([0,T]\)). The proofs are based on properties of functional operators.
reviewed by: Svatoslav Staněk
Mathematics Subject Classification ID: 34K10
Mathematics Subject Classification ID: 34K06
zbMATH DE Number: 1761021
zbMATH Keywords: functional-differential equation
zbMATH Keywords: boundary value problem
zbMATH Keywords: proportional time delays
zbMATH Keywords: solvability
zbMATH Keywords: smoothness of solution
author: L. E. Rossovskii
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1761021