Electron. J. Diff. Eqns., Vol. 2008(2008), No. 108, pp. 1-12.

Large time behavior of solutions to second-order differential equations with p-Laplacian

Milan Medved, Eva Pekarkova

We study asymptotic properties of solutions for certain second-order differential equation with p-Laplacian. The main purpose is to investigate when all global solutions behave at infinity like nontrivial linear functions. Making use of Bihari's inequality and its Dannan's version, we obtain results for differential equations with p-Laplacian analogous which extend those known in the literature concerning ordinary second order differential equations.

Submitted June 9, 2008. Published August 11, 2008.
Math Subject Classifications: 34C11.
Key Words: Second order differential equation; p-Laplacian; Bihari's inequality; asymptotic properties; Dannan's inequality.

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Milan Medved
Department of Mathematical Analysis and Numerical Mathematics
Faculty of Mathematics, Physics and Informatics
Comenius University, Mlynska dolina, 842 48 Bratislava, Slovakia
email: medved@fmph.uniba.sk
Eva Pekarkova
Department of Mathematics and Statistics
Faculty of Science, Masaryk University
Janackovo nam. 2a, CZ-602 00 Brno, Czech Republic
email: pekarkov@math.muni.cz

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