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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On coupled multiparameter nonlinear elliptic systems


Author: Robert Stephen Cantrell
Journal: Trans. Amer. Math. Soc. 294 (1986), 263-285
MSC: Primary 58E07; Secondary 35B32, 35J60
MathSciNet review: 819947
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Abstract: This paper considers the system of nonlinear Dirichlet boundary value problems

$\displaystyle \left\{ \begin{gathered}Lu(x) = \lambda f(u(x),v(x)) \hfill \\ Lv(x) = \mu g(u(x),v(x)) \hfill \\ \end{gathered} \right\},\qquad x \in \Omega ,$

a bounded domain in $ {{\mathbf{R}}^n}$. Here $ L$ is a strongly, uniformly elliptic linear partial differential operator, $ \lambda $, $ \mu $ are real parameters, and $ f$, $ g:{{\mathbf{R}}^2} \to R$ are smooth with

$\displaystyle f(0,0) = 0 = g(0,0).$

A detailed analysis of the solution set to the system is given from the point of view of several parameter bifurcation theory.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1986-0819947-4
PII: S 0002-9947(1986)0819947-4
Article copyright: © Copyright 1986 American Mathematical Society



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