Radial and nonradial solutions for the nonlinear eigenvalue problem \(\Delta u+\lambda e^ u=0\) on annuli in \({\mathbb{R}}^ 2\)
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Publication:2638432
DOI10.1016/0022-0396(90)90020-PzbMath0717.35030MaRDI QIDQ2638432
Ken'ichi Nagasaki, Takashi Suzuki
Publication date: 1990
Published in: Journal of Differential Equations (Search for Journal in Brave)
Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Variational methods for second-order elliptic equations (35J20)
Related Items (17)
Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains ⋮ Mean field equations and domains of first kind ⋮ Symmetry-breaking bifurcation for the one-dimensional Liouville type equation ⋮ Generic properties of the Rabinowitz unbounded continuum ⋮ Existence and multiplicity of positive solutions for elliptic systems ⋮ Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity ⋮ Morse indices and symmetry breaking for the Gelfand equation in expanding annuli ⋮ Radial solutions for \(\Delta{}u+\lambda{}e^ u=0\) on annuli in higher dimensions ⋮ Global bifurcations of solutions of Emden-Fowler-type equation \(-\Delta u(x)=\lambda f(u(x))\) on an annulus in \({\mathbb R}^n\), \(n\geq 3\) ⋮ Global branch from the second eigenvalue for a semilinear Neumann problem in a ball ⋮ On the number of peaks of the eigenfunctions of the linearized Gel'fand problem ⋮ Free boundary problems arising in the theory of maximal solutions of equations with exponential nonlinearities ⋮ Maximal entropy solutions under prescribed mass and energy ⋮ Maximal solution of the Liouville equation in doubly connected domains ⋮ Exact radial solutions for a nonlinear eigenvalue problem ⋮ Analytic imperfect bifurcation theorem and the Liouville-Gel’fand equation on a perturbed annular domain ⋮ On the global bifurcation diagram of the Gelfand problem
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