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Existence, uniqueness, and blow‐up rate of large solutions to equations involving the ∞ − Laplacian on the half line
Author(s) -
Chen Yujuan,
Chen Li
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4327
Subject(s) - uniqueness , mathematics , function (biology) , mathematical analysis , viscosity , laplace operator , viscosity solution , boundary value problem , half line , value (mathematics) , pure mathematics , real line , thermodynamics , statistics , physics , evolutionary biology , biology
This paper shows the existence and the uniqueness of the nonnegative viscosity solution of the singular boundary value problem ( u ′ ( t ) ) 2u′ ′( t ) = f ( t ) h ( u ( t ) ) for t >0, u ( 0 ) = ∞ , u ( ∞ ) = 0 , where f is a continuous non‐decreasing function such that f (0)⩾0, and h is a nonnegative function satisfying the Keller–Osserman condition. Moreover, when h ( u )= u p with p >3, we obtain the global estimates for the classic solution u ( t ) and the exact blow‐up rate of it at t =0. Copyright © 2017 John Wiley & Sons, Ltd.