Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems
In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u), u′(0)=0, βu′(1)+αu(1)=A, where λ is a nonnegative parameter, β≥0, α>0, and A&a...
| 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://dx.doi.org/10.1155/2010/969536 |
| Summary: | In this paper, we investigate the singular Sturm-Liouville problem u′′=λg(u), u′(0)=0, βu′(1)+αu(1)=A, where λ is a nonnegative parameter, β≥0, α>0, and A>0. We discuss the existence of multiple positive solutions and show that for certain values of λ, there also exist solutions that vanish on a subinterval [0,ρ]⊂[0,1), the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u)=1/u and for some model problems from the class of singular differential equations (ϕ(u′))′+f(t,u′)=λg(t,u,u′) discussed in Agarwal et al. (2007). For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied. |
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| ISSN: | 1687-1839 1687-1847 |