Existence and global behavior of positive solution for semilinear problems with boundary blow-up

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:425

Article

Alsaedi, Ramzi¹  Maagli, Habib¹  Zeddini, Noureddine¹ 

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

关键词: Asymptotic behavior;    Positive solution;    Boundary blow-up;    Sub- and supersolutions;   

DOI  :  10.1016/j.jmaa.2014.12.066

来源: Elsevier

【 摘 要 】

Using the sub-supersolution method with Karamata regular variation theory, we study the existence and asymptotic behavior of a classical solution to the following boundary blow-up semilinear Dirichlet problem {Delta u = a(x)f(u), x epsilon ohm, u > 0 in ohm; lim(delta(x)-> 0) u(X) = infinity, where ohm is a C-1,C-1-bounded domain in R-n, n >= 2 and the function a belongs to C-loc(alpha)(ohm), (0 < alpha < 1) such that for each x epsilon ohm, c(1)(delta(x))(-lambda 1) exp(integral(n)(delta(x)) z(1)(s)/sds) <= a(x) <= c(2)(delta(x))(-lambda 2) exp(integral(n)(delta(x)) z(2)(s)/sds), where eta > diam(ohm), c(1) > 0, c(2) > 0, delta(x) = dist(x, partial derivative ohm), lambda(1) <= lambda(2) <= 2 and for i epsilon {1,2}, z(i) is a continuous function on [0, eta] with z(i)(0) = 0. For the function f, we assume that there exist constants kappa(1), kappa(2), p(1), p(2) with 0 < kappa(1) < kappa(2), 1 < p(1) <= p(2) such that f (t) <= k(2)t(p2) for t > 0 and f (t) >= k(1)t(p1) for t >= 1. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free