Open Access Research

On the solvability of a Neumann boundary value problem for the differential equation f ( t , x , x , x ) = 0

P Palamides1, P Kelevedjiev2* and N Popivanov3

Author Affiliations

1 Naval Academy of Greece, Piraeus, 451 10, Greece

2 Department of Mathematics, Technical University of Sliven, Sliven, Bulgaria

3 Faculty of Mathematics and Informatics, ‘St. Kl. Ohridski’ University of Sofia, Sofia, Bulgaria

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Boundary Value Problems 2012, 2012:77  doi:10.1186/1687-2770-2012-77

Published: 23 July 2012

Abstract

Using barrier strip arguments, we investigate the existence of <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M2">View MathML</a>-solutions to the Neumann boundary value problem <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M1">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M4">View MathML</a>, <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/77/mathml/M5">View MathML</a>.

MSC: 34B15.

Keywords:
boundary value problem; equation unsolved with respect to the second derivative; Neumann boundary conditions; existence