Mo, Jiaqi Singularly perturbed semilinear elliptic equations in unbounded domains. (Chinese. English summary) Zbl 0816.35028 J. Math., Wuhan Univ. 12, No. 4, 375-382 (1992). The author considers a boundary value problem for the following semilinear elliptic equation with singular perturbation in an unbounded domain: \[ L_ 2(u)+ \varepsilon L_ 1(u)= f(x,u), \qquad x\in\Omega, \] where \(L_ 2(u)\) is a strictly elliptic operator, \(L_ 1(u)\) is a linear operator, \(\varepsilon>0\) is a perturbation parameter, and \(\Omega\subset \mathbb{R}^ n\) is unbounded. The author proves by means of a differential inequality method under certain conditions that there exists a solution to the above problem and that this solution has an asymptotic expansion, which is uniformly valid in the whole domain. Reviewer: Yu Wenhuan (Tianjin) Cited in 3 Documents MSC: 35J60 Nonlinear elliptic equations 35C20 Asymptotic expansions of solutions to PDEs 35B25 Singular perturbations in context of PDEs Keywords:unbounded domain; semilinear elliptic equation; singular perturbation; asymptotic expansion PDFBibTeX XMLCite \textit{J. Mo}, J. Math., Wuhan Univ. 12, No. 4, 375--382 (1992; Zbl 0816.35028)