Large solutions for non-divergence structure equations with singular lower order terms

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• 作者：Ahmed Mohammed^a ; ^{amohammed@bsu.edu} ; Giovanni Porru^b ; ^{porru@unica.it}
• 关键词：Semi-linear elliptic equations ; Large solutions ; Boundary behavior ; Uniqueness
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：470-482
• 全文大小：590 K
• 卷排序：35

文摘

In this paper we investigate infinite boundary value problems associated with the semi-linear PDE Lu=k(x)f(u)Lu=k(x)f(u) on a bounded smooth domain Ω⊂Rn, where LL is a non-divergence structure, uniformly elliptic operator with singular lower order terms. The weight kk is a continuous non-negative function and ff is a continuous nondecreasing function that satisfies the Keller–Osserman condition. We study a sufficient condition on kk that ensures existence of a large solution uu. In case the lower order terms of LL are bounded, under further assumptions on ff and kk we establish asymptotic bounds of solutions uu near the boundary ∂Ω and, as a consequence a uniqueness result.