Characterization of non-disconjugacy for a one parameter family of n-th order linear differential equations
The aim of this paper is to obtain different criteria which allow us to affirm that the one parameter family of $n^{\mathrm{th}}-$order linear differential equations, given by the following expression \[ T_n[M]\,u(t) \equiv u^{(n)}(t)+a_1(t)\, u^{(n-1)}(t)+\cdots +a_{n-1}(t)\, u'(t)+(a_{n}(t)+M...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universidad de Santiago de Compostela (USC) |
| Repositorio: | Minerva. Repositorio Institucional de la Universidad de Santiago de Compostela |
| Idioma: | inglés |
| OAI Identifier: | oai:minerva.usc.gal:10347/45452 |
| Acceso en línea: | https://hdl.handle.net/10347/45452 |
| Access Level: | acceso abierto |
| Palabra clave: | Disconjugacy Green's functions Spectral theory 1202 Análisis y análisis funcional |
| Sumario: | The aim of this paper is to obtain different criteria which allow us to affirm that the one parameter family of $n^{\mathrm{th}}-$order linear differential equations, given by the following expression \[ T_n[M]\,u(t) \equiv u^{(n)}(t)+a_1(t)\, u^{(n-1)}(t)+\cdots +a_{n-1}(t)\, u'(t)+(a_{n}(t)+M)\,u(t)=0 \,,\quad t\in I\equiv[a,b]\,, \] is not disconjugate for every $M\in \mathbb{R}$. Three different sufficient criteria, which ensure that such property holds, are presented. Moreover, a characterization of this property is given. To finish the paper, three examples, where the different criteria are applied, are shown. |
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