n -th Order Functional Problems with Resonance of Dimension One

Erin Benham and Nickolai Kosmatov
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Erin Benham: Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204-1099, USA
Nickolai Kosmatov: Department of Mathematics and Statistics, University of Arkansas at Little Rock, Little Rock, AR 72204-1099, USA

Mathematics, 2021, vol. 9, issue 19, 1-15

Abstract: We consider the nonlinear n -th order boundary value problem L u = u ( n ) = f ( t , u ( t ) , u ? ( t ) , … , u ( n ? 1 ) ( t ) ) = N u given arbitrary bounded linear functional conditions B i ( u ) = 0 , i = 1 , … , n and develop a method that allows us to study all such resonance problems of order one, as well as implementing a more general constructive method for deriving existence criteria in the framework of the coincidence degree method of Mawhin. We demonstrate applicability of the formalism by giving an example for n = 4 .

Keywords: Carathéodory conditions; coincidence degree theory; functional condition; resonance (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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