Duality theorems for functional differential equations and application to superlinear problems
type: Item
instance of: scholarly article
title: Duality theorems for functional differential equations and application to superlinear problems
zbMATH Open document ID: 0874.34056
author: Marc Henrard
published in: Differential Equations and Dynamical Systems
publication date: 1997-11-13T00:00:00Z
review text: It is shown that the coincidence degree associated with the functional differential equation \[ x''(t)= f\bigl(t,x_t, (x')_t\bigr) \quad x_0+ Nx_1= g(x) \quad h(x)=0 \] can be obtained by the computation of the degree associated with the ordinary differential equation \[ x''(t)= \overline f\bigl(t,x(t), x'(t)\bigr) \quad x(0) + N(x_1)(0) =g(x)(0) \quad h(x)=0 \] where \(f\) and \(h\) are continuous and map bounded sets to bounded sets, \(N\) is linear and continuous, \(g\) is completely continuous and \(f(t,x,y)= \overline f(t,x(0), y(0))\). Some conditions for the existence and multiplicity for superlinear equations are also established.
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 1014357
zbMATH Keywords: coincidence degree
zbMATH Keywords: functional differential equation
zbMATH Keywords: existence and multiplicity
zbMATH Keywords: superlinear equations
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1014357