Theses and Dissertations

Issuing Body

Mississippi State University

Shivaji, Ratnasingham

Lim, Hyeona

Banicescu, Ioana

Miller, Len

Committee Member

Smith, Robert

Oppenheimer, Seth

8-9-2008

Document Type

Dissertation - Open Access

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

Abstract

We study positive solutions to nonlinear elliptic systems of the form: \begin{eqnarray*} -\Delta u =\lambda f(v) \mbox{ in }\Omega\\-\Delta v =\lambda g(u) \mbox{ in }\Omega\\\quad~~ u=0=v \mbox{ on }\partial\Omega \end{eqnarray*} where $\Delta u$ is the Laplacian of $u$, $\lambda$ is a positive parameter and $\Omega$ is a bounded domain in $R^n$ with smooth boundary $\partial\Omega$. In particular, we will analyze the combined effects of the nonlinearities on the existence and multiplicity of positive solutions. We also study systems with multiparameters and stronger coupling. We extend our results to $p$-$q$-Laplacian systems and to $n\times n$ systems. We mainly use sub- and super-solutions to prove our results.

URI

https://hdl.handle.net/11668/15464

$p$-Laplacian||sub-super solutions||multiple solutions||ellitpic systems||positone

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