On nonlinear singular BVPs with nonsmooth data. Part 1: Analytical results

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61989592%3A15310%2F18%3A73586697" target="_blank" >RIV/61989592:15310/18:73586697 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S0168927418300734" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0168927418300734</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.apnum.2018.03.011" target="_blank" >10.1016/j.apnum.2018.03.011</a>

Result language
angličtina
Original language name
On nonlinear singular BVPs with nonsmooth data. Part 1: Analytical results
Original language description
We study boundary value problems for systems of nonlinear ordinary differential equations with a time singularity, x'(t) = M(t)/t x(t) + f(t,x(t))/t, t in(0,1], b(x(0),x(1))=0,where M:[0,1] to R(n x n)and f:[0,1] x Rn to Rn are continuous matrix-valued and vector-valued functions, respectively. Moreover, b: Rn x Rn to Rn is a continuous nonlinear mapping which is specified according to a spectrum of the matrix M(0). For the case that M(0) has eigenvalues with nonzero real parts, we prove new results about existence of at least one continuous solution on the closed interval [0,1] including the singular point, t=0. We also formulate sufficient conditions for uniqueness. The theory is illustrated by a numerical simulation based on the collocation method.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA14-06958S" target="_blank" >GA14-06958S: Singularities and impulses in boundary value problems for nonlinear ordinary differential equations</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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