Existence and global asymptotic behavior of positive solutions for nonlinear problems on the half-line

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:416

Article

Bachar, Imed¹  Maagli, Habib² 

[1] King Saud Univ, Coll Sci, Dept Math, Riyadh 11451, Saudi Arabia

[2] King Abdulaziz Univ, Coll Arts & Sci, Dept Math, Rabigh 21911, Saudi Arabia

关键词: Green function;    Karamata regular variation theory;    Positive solutions;    Monotonicity methods;   

DOI  :  10.1016/j.jmaa.2014.02.029

来源: Elsevier

【 摘 要 】

In this paper, we aim at studying the existence, uniqueness and the exact asymptotic behavior of positive solutions to the following boundary value problem {1/A(Au')' + a(t)u(sigma) = 0, t is an element of (0, infinity), lim(t -> 0+) u(t) = 0, lim(t ->infinity) u(t)/rho(t) = 0, where sigma < 1, A is a continuous function on [0, infinity), positive and differentiable on (0, infinity) such that 1/A is integrable on [0,1] and integral(infinity)(0) 1/A(t) dt = infinity. Here rho(t) = integral(t)(0) 1/A(s) ds, for t >= 0 and a is a nonnegative continuous function that is required to satisfy some assumptions related to the Kararnata classes of regularly varying functions. Our arguments are based on monotonicity methods. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free