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.
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Ghergu, M. (2013). Singular Semilinear Elliptic Equations with Subquadratic Gradient Terms. In: Reissig, M., Ruzhansky, M. (eds) Progress in Partial Differential Equations. Springer Proceedings in Mathematics & Statistics, vol 44. Springer, Heidelberg. https://doi.org/10.1007/978-3-319-00125-8_4
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DOI: https://doi.org/10.1007/978-3-319-00125-8_4
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