Existence of solutions to the nonlinear, singular second order Bohr boundary value problems
type: Item
instance of: scholarly article
title: Existence of solutions to the nonlinear, singular second order Bohr boundary value problems
zbMATH Open document ID: 1367.34023
author: Nicholas Fewster-Young
published in: Nonlinear Analysis. Real World Applications
publication date: 2017-03-30T00:00:00Z
review text: This paper studies the existence of solutions and a priori bounds to the boundary value problem \[ \frac{1}{p(t)}(p(t){\mathbf y'}(t))'=q(t){\mathbf f}(t,{\mathbf y}(t),p(t){\mathbf y'}(t)),\;t\in(0,T), \] \[ {\mathbf y}(0)={\mathbf c},\;\int_0^T\frac{ds}{p(s)}\lim_{t\to T^-}p(t){\mathbf y'}(t)-{\mathbf y}(T)={\mathbf d}, \] where \(p\in C([0,T];R)\cap C^1((0,T);R)\) and \(q\in C((0,T);R)\) are positive on \((0,T)\), \({\mathbf f}\in C([0,T]\times R^n\times R^n; R^n),\) and \(\mathbf {c,d}\in R^n\) are constants. As the author writes in the abstract ``The methodology in this paper uses an alternative and equivalent BVP, which is in the class of resonant singular BVPs, and thus this paper obtains novel results by implementing an innovative differential inequality, Lyapunov functions and topological techniques.''
reviewed by: Petio S. Kelevedjiev
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 6698079
zbMATH Keywords: boundary value problem
zbMATH Keywords: Bohr boundary conditions
zbMATH Keywords: singularity
zbMATH Keywords: resonant BVPs
zbMATH Keywords: existence
MaRDI profile type: Publication
full work available at URL: j.nonrwa.2017.01.009
OpenAlex ID: W2587053221
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DOI: 10.1016/J.NONRWA.2017.01.009
description: scientific article; zbMATH DE number 6698079