A certain functional derivative equation corresponding to \(\square u+cu+bu^ 2+au^ 3=g\) on \(R^{d+1}\)
type: Item
instance of: scholarly article
title: A certain functional derivative equation corresponding to \(\square u+cu+bu^ 2+au^ 3=g\) on \(R^{d+1}\)
zbMATH Open document ID: 0705.35148
author: Atsushi Inoue
published in: Proceedings of the Japan Academy. Series A
publication date: 1989-01-01T00:00:00Z
review text: The author of this short note formulates two problems for functionals and measures, respectively, which are in some sense connected with the Klein- Gordon equation \[ \square u+cu+bu^ 2+au^ 3=g. \] He gives the corresponding notions of solution and conditions for solvability. Proofs are only sketched.
Mathematics Subject Classification ID: 35R15
Mathematics Subject Classification ID: 35L70
zbMATH DE Number: 4157148
zbMATH Keywords: functional derivative equation
zbMATH Keywords: Klein-Gordon equation
MaRDI profile type: Publication
full work available at URL: pjaa.65.35
OpenAlex ID: W2076835823
cites work: Statistical study of Navier-Stokes equations. I
cites work: Strong and classical solutions of the Hopf equation - an example of functional derivative equation of second order
cites work: On the solvability of the Cauchy problem for the Hopf equation corresponding to a nonlinear hyperbolic equation
DOI: 10.3792/PJAA.65.35
Recommended article: On Hopf type functional derivative equations for \(\square{} u+cu+bu^ 2+au^ 3 = 0\) on \(\Omega{} \times{} R\). I: Existence of solutions
Recommended article: On the equation \(A \nabla u + \left( \nabla u\right)^t A = G\)
Recommended article: On the equation \(\Delta u+x\cdot \nabla u+f(u)=0\)
Recommended article: On the functional equation $\displaystyle \alpha\bf{u}+\mathcal{C}\star(\chi \bf{u})=\bf{f}$
Recommended article: Q4018911
Recommended article: On the functional differential equation \(x'(t)=A(t)x(g(t))\)
Recommended article: Q3779103
Recommended article: On a functional equation related to a problem of G. Derfel
Recommended article: On the equation \(\nabla u=uV\)
Recommended article: Solutions of the equation \(\Delta u= f(x,y) e^{cu}\) in some special cases
description: scientific article; zbMATH DE number 4157148