grandes-ecoles 2012 QVII.B

grandes-ecoles · France · centrale-maths1__psi Differential equations Eigenvalue Problems and Operator-Based DEs
In this question, $f(t) = \cos t$ and $\lambda(t) = \ln(1+t)$.
VII.B.1) Determine $E$.
VII.B.2) Determine $E^{\prime}$.
VII.B.3) Show that $Lf$ admits a limit at $\alpha$, the infimum of $E$, and determine it.
In this question, $f(t) = \cos t$ and $\lambda(t) = \ln(1+t)$.

VII.B.1) Determine $E$.

VII.B.2) Determine $E^{\prime}$.

VII.B.3) Show that $Lf$ admits a limit at $\alpha$, the infimum of $E$, and determine it.