PhD Dissertation Defense: "Existence and nonexistence of solutions for semilinear problems on exterior domains" | Department of Mathematics
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PhD Dissertation Defense: "Existence and nonexistence of solutions for semilinear problems on exterior domains"

Event Information
Speaker: 
Janak Joshi
Event Location: 
GAB 461
Event Date: 
Monday, May 21, 2018 - 2:00pm

Professor Joseph Iaia invites you to attend the PhD dissertation defense of Janak Joshi

Monday, May 21st at 2:00pm in GAB 461

"Existence and nonexistence of solutions for semilinear problems on exterior domains"

Abstract:

We prove the existence and non-existence of solutions for the semilinear problem ∆u +K(r) = 0 with various boundary conditions on the exterior of the ball in ℝN such that lim u(r) = 0 as r approaches infinity. Here, f: ℝ → ℝ is an odd locally lipschitz non-linear function such that there exists a β > 0 with f < 0 on (0, β), f > 0 on (β, ∞), and K(r) ∼ r-α for some α > 0.