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n -th Order Functional Problems with Resonance of Dimension One

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Erin Benham & Nickolai Kosmatov, 2021. "n -th Order Functional Problems with Resonance of Dimension One," Mathematics, MDPI, vol. 9(19), pages 1-15, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2384-:d:642847
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