A one-dimensional Kirchhoff equation with generalized convolution coefficients
type: Item
instance of: scholarly article
title: A one-dimensional Kirchhoff equation with generalized convolution coefficients
zbMATH Open document ID: 1504.34052
author: Christopher Goodrich
published in: Journal of Fixed Point Theory and Applications
publication date: 2021-11-25T00:00:00Z
review text: The author studies, by means of classical fixed point index theory, the existence of at least one positive solution of the generalized one-dimensional Kirchhoff-type equation of the form \[ - A((a* (u')^q)(1)) u''(t)=\lambda f(t, u(t))\,\text{for}\, t\in (0,1), \] where \(q\geq 1\), subject to the right-focal boundary conditions \[ u(0)=0,\quad u'(1)=0. \] The choice of the convolution term in the differential equation is very flexible and covers a variety of situations, including fractional derivative coefficients of Caputo type.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B08
Mathematics Subject Classification ID: 34A08
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 7433415
zbMATH Keywords: finite convolution
zbMATH Keywords: Kirchhoff equation
zbMATH Keywords: Caputo fractional derivative
zbMATH Keywords: positive solution
zbMATH Keywords: coercivity
reviewed by: Gennaro Infante
MaRDI profile type: Publication
full work available at URL: s11784-021-00910-z
OpenAlex ID: W3214282449
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A one-dimensional Kirchhoff equation with generalized convolution coefficients (DOI)
DOI: 10.1007/S11784-021-00910-Z