Theses and Dissertations
Issuing Body
Mississippi State University
Advisor
Shivaji, Ratnasingham
Committee Member
Lim, Hyeona
Committee Member
Banicescu, Ioana
Committee Member
Miller, Len
Committee Member
Smith, Robert
Other Advisors or Committee Members
Oppenheimer, Seth
Date of Degree
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
Recommended Citation
Hameed, Jaffar Ali Shahul, "Multiple positive solutions for classes of elliptic systems with combined nonlinear effects" (2008). Theses and Dissertations. 3236.
https://scholarsjunction.msstate.edu/td/3236
Comments
$p$-Laplacian||sub-super solutions||multiple solutions||ellitpic systems||positone