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Calendar

Tuesday, September 21
Mathematics Colloquium: Maximum principles about simple eigenvalues
03:35 PM - 05:35 PM
Location: Science Center Room 323
Cost: Free and open to the public

Abstract: Let "b" be real. The boundary value problem u''+bu=f, with Neumann boundary conditions, u'(0)=0, u'(1)=0, has a simple eigenvalue at b=0, and the eigenfunctions are constant functions. If b<0, the boundary value problem satisfies a maximum principle; in particular, if f is a nonnegative function, then solutions, u, are nonpositive. There exists B>0 such that if 0<b<B, the boundary value problem satisfies an anti-maximum principle; in particular, if f is a nonnegative function, then solutions, u, are nonnegative. Campos, Mawhin and Ortega provide a nice explanation for this change of behavior of maximum principles about simple eigenvalues with constant eigenfunctions. In this talk, we present extensions of their work to problems with simple eigenvalues and non-constant eigenfunctions.

Refreshments will be served at 3:15 at the Mathematics Conference Room 313F.

 

Contact Information:
Name: Muhammad Usman