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Multiple positive solutions for classes of elliptic systems with combined nonlinear effects

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.

Identiferoai:union.ndltd.org:MSSTATE/oai:scholarsjunction.msstate.edu:td-4235
Date09 August 2008
CreatorsHameed, Jaffar Ali Shahul
PublisherScholars Junction
Source SetsMississippi State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceTheses and Dissertations

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