Dirichlet problems for semilinear elliptic equations with a fast growth coefficient on unbounded domains
Texas State University-San Marcos, Department of Mathematics
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.
Elliptic boundary-value problems, Positive solutions, Semilinear equations, Unbounded domains, Perron's method, Super solutions
Jin, 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.
Attribution 4.0 International