Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains
MetadataShow full metadata
When 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.
CitationJin, Z. (2005). Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains. Electronic Journal of Differential Equations, 2005(109), pp. 1-12.
This work is licensed under a Creative Commons Attribution 4.0 International License.