Toronto Math Forum

MAT244-2014F => MAT244 Math--Lectures => Topic started by: Hyunmin Jung on October 29, 2014, 11:44:55 AM

Title: About the existence of solution for linear occasion for first order equation
Post by: Hyunmin Jung on October 29, 2014, 11:44:55 AM
When p(t) is continuous on the interval containing initial t

but g(t) is not continuous on the I containing initial t, it violates theorem 2.4.1 but is unsure whether or

not non-unique solution exist for all t in I? and the case for when g(t) is continuous on the interval and p(t) is not.
Title: Re: About the existence of solution for linear occasion for first order equation
Post by: Victor Ivrii on October 29, 2014, 12:17:44 PM
Linear equations tolerate a lot of abuse (non-smoothness). It does not follow from theorems we studied but there is an uniqueness and existence as long as $g$ is just integrable and $p$ is bounded