@prefix mdl: <http://data.loterre.fr/ark:/67375/MDL> .
@prefix skos: <http://www.w3.org/2004/02/skos/core#> .

mdl:-DPLKJP65-G
  skos:prefLabel "équation différentielle"@fr, "differential equation"@en ;
  a skos:Concept ;
  skos:narrower mdl:-DPH11BV0-N .

mdl: a skos:ConceptScheme .
mdl:-DPH11BV0-N
  skos:hiddenLabel "théories de Sturm-Liouville"@fr, "théorie de Sturm Liouville"@fr, "Equation Sturm Liouville"@fr, "Sturm Liouville equation"@en, "théories de Sturm Liouville"@fr ;
  skos:definition "En mathématiques, la théorie de Sturm-Liouville étudie le cas particulier des équations différentielles linéaires scalaires d'ordre deux de la forme d/dx[p(x)dy/dx] + q(x)y = λ w(x)y (1), dans laquelle le paramètre λ fait partie comme la fonction y des inconnues. La fonction w(x) est souvent appelé fonction \"poids\" ou \"densité\". Cette équation est fréquemment posée sur un segment [a,b] et accompagnée de conditions aux limites reliant les valeurs y(a), y′(a), y(b) et y′(b). (Wikipedia, L'Encylopédie Libre, <a href=\"https://fr.wikipedia.org/wiki/Th%C3%A9orie_de_Sturm-Liouville\" target=\"_blank\">https://fr.wikipedia.org/wiki/Th%C3%A9orie_de_Sturm-Liouville</a>)"@fr, "In mathematics and its applications, classical Sturm–Liouville theory is the theory of real second-order linear ordinary differential equations of the form : d/dx[p(x)dy/dx] + q(x)y = -λ w(x)y (1), for given coefficient functions p(x), q(x), and w(x), an unknown function y = y(x) of the free variable x, and an unknown constant λ. All homogeneous (i.e. with the right-hand side equal to zero) second-order linear ordinary differential equations can be reduced to this form. In addition, the solution y is typically required to satisfy some boundary conditions at extreme values of x. Each such equation together with its boundary conditions constitutes a Sturm–Liouville problem. In the simplest case where all coefficients are continuous on the finite closed interval [a, b] and p has continuous derivative, a function y = y(x) is called a solution if it is continuously differentiable and satisfies the equation (1) at every x ∈ ( a , b ). In the case of more general p(x), q(x), w(x), the solutions must be understood in a weak sense. (Wikipedia, The Free Encyclopedia, <a href=\"https://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville_theory\" target=\"_blank\">https://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville_theory</a>)"@en ;
  skos:broader mdl:-DPLKJP65-G ;
  skos:inScheme mdl: ;
  skos:exactMatch <https://fr.wikipedia.org/wiki/Th%C3%A9orie_de_Sturm-Liouville>, <https://en.wikipedia.org/wiki/Sturm%E2%80%93Liouville_theory> ;
  skos:prefLabel "Sturm-Liouville theory"@en, "théorie de Sturm-Liouville"@fr ;
  a skos:Concept .