Abstract
Using a few conditions, continuous dependence, and a result regarding smoothness of initial conditions, we show that derivatives of solutions to the second order boundary value problem y''=f (x, y, y'), a < x < b, y (x1) = y1, 1 d-c ∫ c d y(x)dx = y2, a < x1 < c < d < b, y1, y2 ∈ ℝ with respect to each of the boundary data x1, y1, y2, c, d solve the associated variational equation with interesting boundary conditions. Of note is the second bundary condition with an average value condition.
Faculty Sponsors
Dr. Jeffrey Lyons
Project Type
Event
Location
Alvin Sherman Library
Start Date
4-7-2017 12:00 AM
End Date
4-7-2017 12:00 AM
Continuous Dependence and Differentiating Solutions of a Second Order Boundary Value Problem with an Average Value Condition
Alvin Sherman Library
Using a few conditions, continuous dependence, and a result regarding smoothness of initial conditions, we show that derivatives of solutions to the second order boundary value problem y''=f (x, y, y'), a < x < b, y (x1) = y1, 1 d-c ∫ c d y(x)dx = y2, a < x1 < c < d < b, y1, y2 ∈ ℝ with respect to each of the boundary data x1, y1, y2, c, d solve the associated variational equation with interesting boundary conditions. Of note is the second bundary condition with an average value condition.
