Toronto Math Forum

APM346-2016F => APM346--Lectures => Chapter 4 => Topic started by: Shaghayegh A on November 14, 2016, 02:03:24 PM

Title: HA 6, problem 1c of sections 4.1 and 4.2
Post by: Shaghayegh A on November 14, 2016, 02:03:24 PM

Problem 1c asks to investigate how many negative eigenvalues there are:
http://www.math.toronto.edu/courses/apm346h1/20169/PDE-textbook/Chapter4/S4.2.P.html#mjx-eqn-a

I understand that we have the hyperbola $$\alpha + \beta+ \alpha \beta l=0$$ which divides the $(\alpha,\beta)$ plane into three zones, as he problem states. But how does that actually help us find the number of negative eigenvalues?

Title: Re: HA 6, problem 1c of sections 4.1 and 4.2
Post by: Victor Ivrii on November 15, 2016, 06:59:42 AM

Look in the textbook:we just need to calculate the number of eigenvalues at the point of our choice in each region