Journal of Advances in Mathematics and Computer Science

Estimates for Boundary Blowup Solutions of p-Laplacian Type Quasilinear Elliptic Equations

Xingbao Lin

Institute of Mathematics, School of Mathematical Sciences, Nanjing Normal University, Jiangsu Nanjing 210023, China.

Zuodong Yang *

School of Teacher Education, Nanjing Normal University, Jiangsu Nanjing 210097, China.

*Author to whom correspondence should be addressed.

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Abstract

In this paper, we investigate the effect of the mean curvature of the boundary ∂Ω on the behavior of the blow-up solutions to the p-Laplacian type quasilinear elliptic equation

                                          div(|∇u|^p-2∇u) = u^m|∇u|, p > 1,

where the Ω ∈ R^N be a bounded smooth domain. Under appropriate conditions on p and m, we find the estimates of the solution u interms of the distance from x to the boundary ∂Ω. To the equation

                                          div(|∇u|^p-2∇u) = u^m|∇u|^q, p > 1, 0 < q < 1,

the results of the semilinear problem are extended to the quasilinear ones.

Keywords: p-Laplacian elliptic equation, boundary blow-up solution, estimates.

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