Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions

Date

2006-01-06

Authors

Zhang, Zhijun

Journal Title

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Volume Title

Publisher

Texas State University-San Marcos, Department of Mathematics

Abstract

We consider the boundary blow-up nonlinear elliptic problems Δu ± λ|∇u|q = k(x)g(u) in a bounded domain with boundary condition u|∂Ω = +∞, where q ∈ [0, 2] and λ ≥ 0. Under suitable growth assumptions on K near the boundary and on g both at zero and at infinity, we show the existence of at least one solution in C2(Ω). Our proof is based on the method of explosive sub-supersolutions, which permits positive weights k(x) which are unbounded and / or oscillatory near the boundary. Also, we show the global optimal asymptotic behaviour of the solution in some special cases.

Description

Keywords

Semilinear elliptic equations, Explosive subsolutions, Explosive superbsolutions, Existence, Global optimal asymptotic behaviour

Citation

Zhang, Z. (2006). Existence of large solutions for a semilinear elliptic problem via explosive sub- supersolutions. Electronic Journal of Differential Equations, 2006(02), pp. 1-8.

Rights

Attribution 4.0 International

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