Quinn Morris

Quinn Morris
Appalachian State University | ASU · Department of Mathematical Sciences

Doctor of Philosophy

About

10
Publications
771
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70
Citations
Additional affiliations
August 2018 - present
Appalachian State University
Position
  • Professor (Assistant)
August 2018 - present
Appalachian State University
Position
  • Professor (Assistant)
August 2017 - July 2018
Swarthmore College
Position
  • Professor (Assistant)
Description
  • Teaching introductory and upper divisional courses in the Department of Mathematics & Statistics
Education
August 2012 - August 2017
University of North Carolina at Greensboro
Field of study
  • Computational Mathematics
August 2010 - May 2012
Wake Forest University
Field of study
  • Mathematics
August 2006 - May 2010
Wake Forest University
Field of study
  • Mathematics

Publications

Publications (10)
Article
Positone and semipositone boundary value problems are semilinear elliptic partial differential equations (PDEs) that arise in reaction diffusion models in mathematical biology and the theory of nonlinear heat generation. Under certain conditions, the problems may have multiple positive solutions or even nonexistence of a positive solution. We devel...
Article
We study positive solutions to the steady state reaction diffusion equation: (formula present) where Ω0 is a bounded domain in ℝ ⁿ ; n≥1 with smooth boundary ∂Ω 0 , ∂/∂ η is the outward normal derivative, A∈(0,1) is a constant, and λ, γ are positive parameters. Such models arise in the study of population dynamics when the population exhibits a U-s...
Article
Full-text available
We analyze the positive solutions to {−Δv=λv(1−v);Ω0,∂v∂η+γλv=0;∂Ω0,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \textstyle\begin{cases} - \Delta v = \lambda v(1-v)...
Article
We prove the existence of positive radial solutions to a class of semipositone p -Laplacian problems on the exterior of a ball subject to Dirichlet and nonlinear boundary conditions. Using variational methods we prove the existence of a solution, and then use a priori estimates to prove the positivity of the solution.
Article
Full-text available
We discuss a quadrature method for generating bifurcation curves of positive solutions to some autonomous boundary value problems with nonlinear boundary conditions. We consider various nonlinearities, including positone and semipositone problems in both singular and nonsingular cases. After analyzing the method in these cases, we provide an algori...
Article
We study positive radial solutions to where is a parameter, , Δ is the Laplacian operator, satisfies for , and is a class of non-decreasing functions satisfying (superlinear) and (semipositone). We consider solutions, u, such that as , and which also satisfy the nonlinear boundary conditon when , where is the outward normal derivative, and . We wil...
Article
Full-text available
We prove the existence of solutions for the boundary-value problem -u ''' =au + -bu - +g(u),u(0)=u(2π),u ' (0)=u ' (2π), where (a,b)∈ℝ 2 , u + (x)=max{u(x),0}, u ( x)=max{-u(x),0}, and g:ℝ→ℝ is a bounded, continuous function. We consider both the resonance and nonresonance cases relative to the Fučík spectrum. For the resonance case we assume a gen...
Article
Full-text available
Solutions to systems of dierential equations which model disease transmission are of particular use and importance to epidemiologists who wish to study eective means to slow and prevent the spread of disease. In this paper, we examine a system that models two related diseases within a population, which is of particular importance to those studying...

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