Asymptotic behavior of boundary blow-up solutions to elliptic equations

作者：Huang, Shuibo^*

来源：Zeitschrift fur Angewandte Mathematik und Physik, 2016, 67(1): 3.

DOI：10.1007/s00033-015-0606-y

• Boundary blow-up solutions
• Asymptotic behavior
• Second-order estimate
• Karamata regular variation theory

This paper is concerned with the asymptotic behavior on partial derivative ohm of boundary blow-up solutions to semilinear elliptic equations
{ Delta u = b(x)f( u), x is an element of Omega, u(x) = infinity, x is an element of partial derivative Omega,
where b(x) is a nonnegative function on Omega and may vanish on. partial derivative Omega at a very degenerate rate; f is nonnegative function on [0, infinity) and normalized regularly varying or rapidly varying at infinity. The main feature of this paper is to establish a unified and explicit asymptotic formula when the function f is normalized regularly varying or grows faster than any power function at infinity. The effect of the mean curvature of the nearest point on the boundary in the second-order approximation of the boundary blow-up solution is also discussed. Our analysis relies on suitable upper and lower solutions and the Karamata regular variation theory.

• 出版日期2016-3
• 单位西北民族大学