Existence, uniqueness, and blow‐up rate of large solutions to equations involving the ∞−Laplacian on the half line. (16th February 2017)

• Record Type: Journal Article
• Authors: Chen, Yujuan; Chen, Li
• Is Part Of: Mathematical methods in the applied sciences. Volume 40:Number 12(2017)
• Page Start: 4577
• Page End: 4594
• Publication Date: 2017-02-16
• Subjects: degenerate elliptic equations -- viscosity solutions -- one‐dimensional infinity Laplacian -- existence and uniqueness -- blow‐up rates; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.4327
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : This paper shows the existence and the uniqueness of the nonnegative viscosity solution of the singular boundary value problem ( u ′ ( t ) ) 2 u ′ ′ ( 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.