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Zbl 1137.35371
Yang, Zuodong; Xu, Bing; Wu, Mingzhu
Existence of positive boundary blow-up solutions for quasilinear elliptic equations via sub and supersolutions.
(English)
[J] Appl. Math. Comput. 188, No. 1, 492-498 (2007). ISSN 0096-3003

Summary: In this paper, the existence of a positive boundary blow-up weak solution for the quasilinear elliptic equation $$\text{div}(\vert \nabla u\vert \sp {p-2}\nabla u)=m(x)f(u)$$ in a smooth bounded domain $\Omega\subset \Bbb R\sp N$ as well as on the whole space $\Omega=\Bbb R\sp N$ is obtained under new conditions. Our proof is based on the method of sub- and super-solutions.
MSC 2000:
*35J60 Nonlinear elliptic equations
35B40 Asymptotic behavior of solutions of PDE
35D05 Existence of generalized solutions of PDE

Keywords: quasilinear elliptic equation; boundary blow-up; sub and supersolutions; Keller-Osserman condition; comparison principle

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