Boundary behaviour of explosive solution to quasilinear elliptic problems with nonlinear gradient terms

Abstract

Based on the Karamata regular variation theory and the method of explosive sub and supersolution, the boundary behaviour of explosive solutions to the quasilinear elliptic equation was obtained, where the singular weight function is non-negative and non-trivial, which may be unbounded on the boundary, the nonlinear term is a Γ-varying function, whose variation at infinity is not regular. The results of this article emphasize the central role played by the gradient term and singular weight function.

Keywords:

• explosive solution
• nonlinear gradient terms
• karamata regular variation theory

AMS Subject Classifications::

• Primary 35B40
• Secondary 35J25