Seventh Mississippi State - UAB Conference on Differential Equations and Computational Simulations. Electron. J. Diff. Eqns., Conference 17 (2009), pp. 71-80.

Existence of three solutions for a higher-order boundary-value problem

John R. Graef, Lingju Kong, Qingkai Kong

Abstract:
We consider a higher-order multi-point boundary-value problem with a nonlinear boundary condition. Sufficient conditions are obtained for the existence of three solutions. In our problem, the differential equation has dependence on all lower order derivatives of the unknown function and the boundary condition covers many multi-point boundary conditions studied earlier by other authors. Our results extend some recent work in the literature.

Published April 15, 2009.
Math Subject Classifications: 34B15, 34B18.
Key Words: Solutions; boundary value problems; lower and upper solutions; Nagumo condition; degree theory.

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John R. Graef
Department of Mathematics
the University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA
email: John-Graef@utc.edu
Lingju Kong
Department of Mathematics
the University of Tennessee at Chattanooga
Chattanooga, TN 37403, USA
email: Lingju-Kong@utc.edu
Qingkai Kong
Department of Mathematics, Northern Illinois University
DeKalb, IL 60115, USA
email: kong@math.niu.edu

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