On equivalent conditions for the solvability of the equation \((p(t)x')'+f(t,x)=h(t)\) satisfying linear boundary conditions with \(f\) restricted by linear growth conditions
type: Item
instance of: scholarly article
title: On equivalent conditions for the solvability of the equation \((p(t)x')'+f(t,x)=h(t)\) satisfying linear boundary conditions with \(f\) restricted by linear growth conditions
zbMATH Open document ID: 0985.34013
published in: Journal of Mathematical Analysis and Applications
publication date: 2001-05-08T00:00:00Z
review text: The author examines the existence of solutions to nonlinear second-order boundary value problems with linear boundary conditions on finite intervals. The concept of generalized resonant point is introduced to generalize the term resonance point (natural frequency or eigenvalue) for the case of linear analogues. The nonlinearity in the differential equation is assumed to be of the form of a Carathéodory function. The solvability of the problem is investigated, and an existence theorem is proved. For some particular cases of the problem, sufficient conditions for the existence of solutions are provided.
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 70K30
Mathematics Subject Classification ID: 34L30
zbMATH DE Number: 1449172
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: generalized resonance point
zbMATH Keywords: existence of solutions
zbMATH Keywords: Carathéodory function
author: Yujun Dong
reviewed by: Nikolai L. Vulchanov
MaRDI profile type: Publication
full work available at URL: jmaa.2000.6752
OpenAlex ID: W1968094197
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DOI: 10.1006/JMAA.2000.6752
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description: scientific article; zbMATH DE number 1449172