Please use this identifier to cite or link to this item: http://hdl.handle.net/10077/16203
Title: On the existence of nontrivial solutions of differential equations subject to linear constraints
Authors: Schmitt, Klaus
Keywords: second order ode’snonlinear multi-point boundary value problemlinear constraintsglobal bifurcation
Issue Date: 2017
Publisher: EUT Edizioni Università di Trieste
Source: Klaus Schmitt, "On the existence of nontrivial solutions of differential equations subject to linear constraints", in: "Rendiconti dell’Istituto di Matematica dell’Università di Trieste. An International Journal of Mathematics", 49 (2017), Trieste, EUT Edizioni Università di Trieste, 2017, pp. 27-40
Journal: Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics 
Part of: 49 (2017)
Abstract: The purpose of this paper is to consider boundary value problems for second order ordinary diff erential equations where the solutions sought are subject to a host of linear constraints (such as multipoint constraints) and to present a unifying framework for studying such. We show how Leray-Schauder continuation techniques may be used to obtain existence results for nontrivial solutions of a variety of nonlinear second order diff erential equations. A typical example may be found in studies of the four-point boundary value problem for the diff erential equation y’’(t)+a(t)f(y(t)) = 0 on [0, 1], where the values of y at 0 and 1 are each some multiple of y(t) at two interior points of (0, 1). The techniques most often used in such studies have their origins in fixed point theory. By embedding such problems into parameter dependent ones, we show that detailed information may be obtained via global bifurcation theory. Of course, such techniques, as they are consequences of properties of the topological degree, are similar in nature.
URI: http://hdl.handle.net/10077/16203
ISSN: 0049-4704
eISSN: 2464-8728
DOI: 10.13137/2464-8728/16203
Rights: Attribution-NonCommercial-NoDerivatives 4.0 Internazionale
Appears in Collections:Rendiconti dell’Istituto di matematica dell’Università di Trieste: an International Journal of Mathematics vol.49 (2017)

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