# Asymptotic integration of differential equations with singular $p$-Laplacian

## Milan Medveď and Eva Pekárková

Address:

Department of Mathematical and Numerical Mathematics, Faculty of Mathematics, Physics and Informatics, Comenius University, Mlynská dolina, 842 48 Bratislava, Slovakia

Institute of Manufacturing Technology, Faculty of Mechanical Engineering, Brno University of Technology, Technická 2896/2, 616 69 Brno, Czech Republic

E-mail:

Milan.Medved@fmph.uniba.sk

pekarkova@fme.vutbr.cz

Abstract: In this paper we deal with the problem of asymptotic integration of nonlinear differential equations with $p-$Laplacian, where $1 < p < 2$. We prove sufficient conditions under which all solutions of an equation from this class are converging to a linear function as $t \rightarrow \infty $.

AMSclassification: primary 34D05; secondary 35B40.

Keywords: $p$-Laplacian, differential equation, asymptotic integration.

DOI: 10.5817/AM2016-1-13