Existence, uniqueness, and blow‐up rate of large solutions to equations involving the   ∞  −  Laplacian on the half line | Zendy

Chen Yujuan | Zendy; Chen Li | Zendy

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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.

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