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Solvability of right focal boundary value problems with superlinear growth conditions

Minghe Pei1, Sung Kag Chang2* and Young Sun Oh3

Author Affiliations

1 Department of Mathematics, Beihua University, JiLin City, 132013, P.R. China

2 Department of Mathematics, Yeungnam University, Kyongsan, 712-749, Korea

3 Department of Mathematics Education, Daegu University, Kyongsan, 712-714, Korea

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Boundary Value Problems 2012, 2012:60  doi:10.1186/1687-2770-2012-60

Published: 22 June 2012

Abstract

In this paper, we consider nth-order two-point right focal boundary value problems

where <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M2">View MathML</a> is a <a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M3">View MathML</a>-Carathéodory (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2012/1/60/mathml/M4">View MathML</a>) function and satisfies superlinear growth conditions. The existence and uniqueness of solutions for the above right focal boundary value problems are obtained by Leray-Schauder continuation theorem and analytical technique. Meanwhile, as an application of our results, examples are given.

MSC: 34B15.

Keywords:
right focal boundary value problem; Leray-Schauder continuation theorem; existence; uniqueness