Nagasaki, Ken’ichi; Suzuki, Takashi Asymptotic analysis for two-dimensional elliptic eigenvalue problems with exponentially dominated nonlinearities. (English) Zbl 0726.35011 Asymptotic Anal. 3, No. 2, 173-188 (1990). In this interesting paper the asymptotic behaviour of solutions \(for\) -\(\Delta\) u\(=\lambda f(u)\), \(u>0\) in \(\Omega\), \(u=0\) on \(\partial \Omega\), \(\lambda\to 0\), is studied, where f(u) is an exponentially dominated nonlinear function. Especially the proved theorems deal with cases of uniform convergence, m-point blow up, entire blow up and with relations for blow up points. Some corollaries concerning special cases (\(\Omega\) star-shaped or convex) are added. In some proofs complex analysis is widely used. Reviewer: A.Göpfert (Merseburg) Cited in 83 Documents MSC: 35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs 35J60 Nonlinear elliptic equations Keywords:uniform convergence; blow up PDFBibTeX XMLCite \textit{K. Nagasaki} and \textit{T. Suzuki}, Asymptotic Anal. 3, No. 2, 173--188 (1990; Zbl 0726.35011)