Jin, Zhiren2021-06-222021-06-222005-10-10Jin, Z. (2005). Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains. <i>Electronic Journal of Differential Equations, 2005</i>(109), pp. 1-12.1072-6691https://hdl.handle.net/10877/13781When an unbounded domain is inside a slab, existence of a positive solution is proved for the Dirichlet problem of a class of semilinear elliptic equations that are similar either to the singular Emden-Fowler equation or a sublinear elliptic equation. The result obtained can be applied to equations with coefficients of the nonlinear term growing exponentially. The proof is based on the super and sub-solution method. A super solution itself is constructed by solving a quasilinear elliptic equation via a modified Perron's method.Text12 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic boundary-value problemsPositive solutionsSemilinear equationsUnbounded domainsPerron's methodSuper solutionsArticle