A second-order estimate for blow-up solutions of elliptic equations

作者：Huang Shuibo^*; Tian Qiaoyu; Zhang Shengzhi; Xi Jinhua

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(6): 2342-2350.

DOI：10.1016/j.na.2010.11.037

• Boundary blow-up solutions
• Second-term asymptotic behavior
• Karamata regular variation theory

We investigate second-term asymptotic behavior of boundary blow-up solutions to the problems Delta u = b(x)f(u), x is an element of Omega, subject to the singular boundary condition u(x) = infinity, in a bounded smooth domain Omega subset of R(N).b(x) is a non-negative weight function. The nonlinearly f is regularly varying at infinity with index rho > 1 (that is lim(u ->infinity) f(xi u)/f(u) = xi(rho) for every xi > 0) and the mapping f(u)/u is increasing on (0, +infinity). The main results show how the mean curvature of the boundary partial derivative Omega appears in the asymptotic expansion of the solution u(x). Our analysis relies on suitable upper and lower solutions and the Karamata regular variation theory.

• 出版日期2011-3-15
• 单位甘肃民族师范学院