Existence And Asymptotical Behavior Of Explosive Solutions For A Class Of Nonlinear Elliptic Equations

In this paper, we show the existence, uniqueness and the exact asymptotic behavior of the class of nonlinear elliptic problemsFirstly, by the sub-super solution method, we obtain the explosive super-solutions and explosive sub-solutions and prove the existence of explosive solutions on a bounded domain, then we prove the existence of global explosive solutions to an unbounded domain by the perturbed method. In addition to, constructing the comparision functions,we apply Karamata regular variation theory and the Cirstea and Radulescu’s argument, to show the exact asymptotical behavior of the large solutions near the boundary to the nonlinear elliptic equations.