Estimations of noncontinuable solutions of second order differential equations with $p$-Laplacian

Eva Pekárková

Address: Department of Mathematics and Statistics, Faculty of Science, Masaryk University Kotlářská 2, 611 37 Brno, Czech Republic

E-mail: evapek@centrum.cz

Abstract: We study asymptotic properties of solutions for a system of second differential equations with $p$-Laplacian. The main purpose is to investigate lower estimates of singular solutions of second order differential equations with $p$-Laplacian $(A(t)\Phi _{p}(y^{\prime }))^{\prime }+B(t)g(y^{\prime })+R(t)f(y)=e(t)$. Furthermore, we obtain results for a scalar equation.

AMSclassification: primary 34C11.

Keywords: second order differential equation, p-Laplacian, asymptotic properties, lower estimate, singular solution.