Electron. J. Diff. Equ., Vol. 2012 (2012), No. 01, pp. 1-9.

Picone-type inequality and Sturmian comparison theorems for quasilinear elliptic operators with p(x)-Laplacians

Norio Yoshida

A Picone-type inequality for quasilinear elliptic operators with mixed nonlinearities and with p(x)-Laplacian is established, and Sturmian comparison theorems are derived on the basis of the Picone-type inequality. Generalizations to more general quasilinear elliptic operators with p(x)-Laplacians and specializations to quasilinear ordinary differential operators with p(t)-Laplacians are shown.

Submitted November 2, 2011. Published January 2, 2012.
Math Subject Classifications: 35B05, 35J92
Key Words: p(x)-Laplacian; Picone-type inequality; quasilinear elliptic operators; Sturmian comparison theorem; mixed nonlinearities.

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Norio Yoshida
Department of Mathematics, University of Toyama
Toyama, 930-8555 Japan
email: nori@sci.u-toyama.ac.jp

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