Existence and optimal estimates of solutions for singular nonlinear Dirichlet problems

✍ Scribed by Zhijun Zhang; Jiangang Cheng

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 230 KB
• Volume: 57
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2004.02.025

✦ Synopsis

By applying the properties of the unique classical solution to the singular boundary value problem on half line -p (s) = g(p(s)); p(s) ¿ 0; s ∈ (0; ∞); p(0) = 0; lims→∞p (s) = b ¿ 0, and constructing the new comparison functions, they show the existence and the optimal global estimates of solutions to singular nonlinear Dirichlet problems -u = k(x)g(u); u ¿ 0; x ∈ ; u| @ = 0, where is a bounded domain with smooth boundary in R N ; g(s) is nonincreasing and positive in (0; ∞); ∞ 1 g(t) dt ¡ ∞ and lim s→0 + g(s) = +∞; k ∈ C ( ) is positive in , and may be singular or zero on the boundary.