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Singular Semilinear Elliptic Equations with Subquadratic Gradient Terms

  • Marius GherguEmail author
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 44)

Abstract

We investigate the semilinear elliptic equation −Δu=a(δ(x))g(u)+f(x,u)+λ|∇u| q in a smooth and bounded domain Ω subject to an homogeneous Dirichlet boundary condition. Here g is an unbounded decreasing function, a is positive and continuous, f grows at most linearly at infinity, \(\delta(x)=\operatorname{dist}(x,\partial\varOmega)\) and 0<q≤2. We emphasize the effect of all these terms in the study of existence, nonexistence and asymptotic behavior of positive solutions.

Keywords

Singular semi-linear equations Gradient term 

Mathematics Subject Classification

35J15 35J75 

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Copyright information

© Springer International Publishing Switzerland 2013

Authors and Affiliations

  1. 1.School of Mathematical SciencesUniversity College DublinDublinIreland

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