Existence and asymptotic behavior of entire blow-up solutions for quasilinear elliptic equation

Abstract

In this article, we discuss the blow-up problem of entire solutions of a class of second-order quasilinear elliptic equation Δ _p u ≡ div(|∇u| ^p−2∇u) = ρ(x)f(u), x ∈ R ^N . No monotonicity condition is assumed upon f(u). Our method used to get the existence of the solution is based on sub-and supersolutions techniques.

Keywords:

• Existence
• Entire blow-up solution
• Quasilinear elliptic equation
• Sub-and supersolutions

2000 AMS Subject Classifications: :

• 35J25
• 35J65
• 35J70

Acknowledgements

This work was partly supported by the Fundamental Research Fund for Physics and Mathematics of Lanzhou University. The authors are also grateful to the reviewer for comments and suggestions which contributed to improve this article.