Events
Applied Mathematics Seminar |
| Time: Feb 28, 2014 (02:00 PM) |
| Location:
Speaker: Paul Schmidt Title: Oscillatory Entire Solutions of Polyharmonic Equations with Power Nonlinearities Abstract: There is a vast amount of literature on positive entire solutions (or "ground states") of semilinear elliptic equations with superlinear growth, with numerous results concerning the existence, uniqueness or multiplicity, and asymptotic behavior of such solutions. Typically, positive entire solutions do not exist if the growth of the nonlinearity is subcritical in a certain sense. A natural question, then, is whether there are sign-changing entire solutions in such cases. I will present recent and ongoing work with Monica Lazzo (University of Bari, Italy) on the existence, uniqueness up to scaling and symmetry, and asymptotic behavior of oscillatory entire radial solutions for a subcritical biharmonic equation with power nonlinearity. Time allowing, I will also discuss possible generalizations to the polyharmonic case. |
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Details: Speaker: Paul Schmidt Title: Oscillatory Entire Solutions of Polyharmonic Equations with Power Nonlinearities Abstract: There is a vast amount of literature on positive entire solutions (or "ground states") of semilinear elliptic equations with superlinear growth, with numerous results concerning the existence, uniqueness or multiplicity, and asymptotic behavior of such solutions. Typically, positive entire solutions do not exist if the growth of the nonlinearity is subcritical in a certain sense. A natural question, then, is whether there are sign-changing entire solutions in such cases. I will present recent and ongoing work with Monica Lazzo (University of Bari, Italy) on the existence, uniqueness up to scaling and symmetry, and asymptotic behavior of oscillatory entire radial solutions for a subcritical biharmonic equation with power nonlinearity. Time allowing, I will also discuss possible generalizations to the polyharmonic case. |