# Quinn MorrisAppalachian State University | ASU · Department of Mathematical Sciences

Quinn Morris

Doctor of Philosophy

## About

10

Publications

798

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76

Citations

Citations since 2016

Introduction

Additional affiliations

Education

August 2012 - August 2017

August 2010 - May 2012

August 2006 - May 2010

## Publications

Publications (10)

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...

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...

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)...

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.

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...

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...

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...

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...