IJPAM: Volume 99, No. 4 (2015)

ASYMPTOTIC BEHAVIOUR OF THE WRONSKIAN OF
BOUNDARY CONDITION FUNCTIONS FOR
A FOURTH ORDER BOUNDARY VALUE
ROBLEM (A SPECIAL CASE)

Emmanuel K. Essel$^1$, Ernest Yankson$^2$, Samuel M. Naandam$^3$, Albert Sackitey Lanor$^4$
$^{1,2,3,4}$Department of Mathematics and Statistics
University of Cape Coast
Cape Coast, GHANA


Abstract. In this paper, we prove that the Wronskian $W\left( \lambda \right) $ of the boundary condition functions for the following boundary value problem $\pi $:

\begin{displaymath}\pi :L\phi \equiv \phi ^{\left( 4\right) }\left( x\right) +P_... ...( x\right) \phi \left( x\right) =\lambda \phi \left( x\right) \end{displaymath}


\begin{displaymath}\phi \left( a\right) =\phi ^{/}\left( a\right) =\phi \left( b\right) =\phi ^{/}\left( b\right) =0\end{displaymath}

is asymptotically equivalent for large values of $\left\vert \lambda \right\vert $, to the Wronskian of the boundary condition functions of the corresponding Fourier problem $\pi _{F}$ given by

\begin{displaymath}\ \pi _{F}:\phi ^{\left( 4\right) }\left( x\right) =\lambda \phi \left( x\right),\end{displaymath}


\begin{displaymath}\phi \left( a\right) =\phi ^{/}\left( a\right) =\phi \left( b\right) =\phi ^{/}\left( b\right) =0.\end{displaymath}



Received: August 23, 2014

AMS Subject Classification: 35B40, 34B05

Key Words and Phrases: Wronskian, Boundary condition functions, fourth order boundary value problem and asymptotic behavior

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DOI: 10.12732/ijpam.v99i4.6 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2015
Volume: 99
Issue: 4
Pages: 455 - 469


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