Large solutions for quasilinear elliptic equation with nonlinear gradient term |
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Authors: | Yujuan Chen Mingxin Wang |
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Affiliation: | 1. Department of Mathematics, Nantong University, Nantong 226007, PR China;2. Natural Science Research Center, Harbin Institute of Technology, Harbin 150080, PR China |
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Abstract: | We study the existence, asymptotic behavior near the boundary and uniqueness of large solutions for a class of quasilinear elliptic equation with a nonlinear gradient term. By constructing the suitable blow-up upper and lower solutions, we obtain the existence and the asymptotic behavior of radial large solutions of the problem in balls and then derive the existence of solutions in a general domain by a comparison argument. By using a perturbation method and constructing comparison functions, we show the exact asymptotic behavior of any nonnegative solution of it near the boundary. The uniqueness is shown by a standard argument. |
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