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MULTIPLE SOLUTIONS FOR A QUASILINEAR ELLIPTIC VARIATIONAL SYSTEM ON STRIP-LIKE DOMAINS

Published online by Cambridge University Press:  08 January 2008

F. Cammaroto ,
A. Chinní  and
B. Di Bella
F. Cammaroto
Affiliation:
Department of Mathematics, University of Messina, Salita Sperone 31, 98166 Sant'Agata-Messina, Italy ([email protected])
A. Chinní
Affiliation:
Department of Mathematics, University of Messina, Salita Sperone 31, 98166 Sant'Agata-Messina, Italy ([email protected])
B. Di Bella
Affiliation:
Department of Mathematics, University of Messina, Salita Sperone 31, 98166 Sant'Agata-Messina, Italy ([email protected])
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Abstract

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We consider the quasilinear elliptic variational system

\begin{alignat*} {2} -\Delta_pu\amp=\lambda F_u(x,u,v)+\mu H_u(x,u,v) \quad\amp \amp\text{in }\varOmega, \\ -\Delta_qv\amp=\lambda F_v(x,u,v)+\mu H_v(x,u,v) \amp \amp \text{in }\varOmega, \\ u\amp=v=0 \amp \amp \text{on }\partial\varOmega, \end{alignat*}

where $\varOmega$ is a strip-like domain and $\lambda$ and $\mu$ are positive parameters. Using a recent two-local-minima theorem and the principle of symmetric criticality, existence and multiplicity are proved under suitable conditions on $F$.

Keywords

Primary 35A15, 35J65Secondary 35P30Strip-like domaineigenvalue problemelliptic systems
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 50 , Issue 3 , October 2007 , pp. 597 - 603
Copyright
Copyright © Edinburgh Mathematical Society 2007