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Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity. (English) Zbl 0785.35045
Summary: For the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) in \(\Omega\subset\mathbb{R}^ 2\), the connectivity of the trivial solution and the one-point blow-up singular limit is studied with respect to the parameter \(\lambda>0\). The connectivity is assured when the domain \(\Omega\) is simply connected and the total mass \(\sum=\int_ \Omega\lambda e^ udx\) tends to \(8\pi\) from below, which is a generalization for the case that \(\Omega\) is a ball.

MSC:
35J65 Nonlinear boundary value problems for linear elliptic equations
47J10 Nonlinear spectral theory, nonlinear eigenvalue problems
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
35J60 Nonlinear elliptic equations
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