Solvability of some pendulum-type equations with linear damping and homogeneous Dirichlet conditions
type: Item
instance of: scholarly article
title: Solvability of some pendulum-type equations with linear damping and homogeneous Dirichlet conditions
zbMATH Open document ID: 1019.34016
DOI: 10.1016/S0362-546X(01)00736-2
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2002-08-25T00:00:00Z
review text: Using a Lyapunov-Schmidt reduction, the authors study the solvability of the nonlinear boundary value problem of pendulum-type \[ -u'' - \alpha u' - \lambda_1(\alpha)y + g(u) = h(x), \quad u(0) = u(\pi) = 0, \] where \(\lambda_1(\alpha) = 1 + \alpha^2/4\) and \(g\) is continuous, \(T\)-periodic and has mean value zero. The results are based upon a delicate asymptotic analysis of the bifurcation equations.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47H11
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D05
zbMATH DE Number: 1787991
zbMATH Keywords: pendulum-type equation
author: Antonio Cañada
author: Antonio J. Ureña
reviewed by: Jean Mawhin
MaRDI profile type: Publication
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full work available at URL: s0362-546x(01)00736-2
OpenAlex ID: W1987089026
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description: scientific article; zbMATH DE number 1787991