Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems
<p/> <p>In this paper, we investigate the singular Sturm-Liouville problem <inline-formula><graphic file="1687-1847-2010-969536-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-969536-i2.gif"/></inline-formula&...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Advances in Difference Equations |
| Online Access: | http://www.advancesindifferenceequations.com/content/2010/969536 |
| Summary: | <p/> <p>In this paper, we investigate the singular Sturm-Liouville problem <inline-formula><graphic file="1687-1847-2010-969536-i1.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-969536-i2.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-969536-i3.gif"/></inline-formula>, where <inline-formula><graphic file="1687-1847-2010-969536-i4.gif"/></inline-formula> is a nonnegative parameter, <inline-formula><graphic file="1687-1847-2010-969536-i5.gif"/></inline-formula>, <inline-formula><graphic file="1687-1847-2010-969536-i6.gif"/></inline-formula>, and <inline-formula><graphic file="1687-1847-2010-969536-i7.gif"/></inline-formula>. We discuss the existence of multiple positive solutions and show that for certain values of <inline-formula><graphic file="1687-1847-2010-969536-i8.gif"/></inline-formula>, there also exist solutions that vanish on a subinterval <inline-formula><graphic file="1687-1847-2010-969536-i9.gif"/></inline-formula>, the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for <inline-formula><graphic file="1687-1847-2010-969536-i10.gif"/></inline-formula> and for some model problems from the class of singular differential equations <inline-formula><graphic file="1687-1847-2010-969536-i11.gif"/></inline-formula> discussed in Agarwal et al. (2007). For the numerical simulation, the collocation method implemented in our MATLAB code <monospace>bvpsuite</monospace> has been applied.</p> |
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| ISSN: | 1687-1839 1687-1847 |