Electron. J. Diff. Equ., Vol. 2013 (2013), No. 128, pp. 1-10.

Lyapunov-type inequalities for nonlinear systems involving the $(p_1,p_2,\dots,p_n)$-Laplacian

Devrim Cakmak, Mustafa Fahri Aktas, Aydin Tiryaki

We prove some generalized Lyapunov-type inequalities for n-dimensional Dirichlet nonlinear systems. We extend the results obtained by Cakmak and Tiryaki [6] for a parameter $1<p_k<2$. As an application, we obtain lower bounds for the eigenvalues of the corresponding system.

Submitted August 20, 2012. Published May 27, 2013.
Math Subject Classifications: 26D10, 34A40, 34C10.
Key Words: Lyapunov-type inequality; lower bound; $(p_1,p_2,\dots,p_n)$-Laplacian.

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Devrim Cakmak
Gazi University, Faculty of Education
Department of Mathematics Education
06500 Teknikokullar, Ankara, Turkey
email: dcakmak@gazi.edu.tr
Mustafa Fahri Aktas
Gazi University, Faculty of Sciences
Department of Mathematics
06500 Teknikokullar, Ankara, Turkey
email: mfahri@gazi.edu.tr
Aydin Tiryaki
Izmir University, Faculty of Arts and Sciences
Department of Mathematics and Computer Sciences
35350 Uckuyular, Izmir, Turkey
email: aydin.tiryaki@izmir.edu.tr

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