Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains

DOI10.1007/BF01459770zbMath0799.35086OpenAlexW1972671559MaRDI QIDQ1327091

Takashi Suzuki, Ken'ichi Nagasaki

Publication date: 15 June 1994

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/165196

zbMATH Keywords

phase plane analysisDirichlet boundary conditionsradially symmetric solutionsEmden-Fowler equationnonradial bifurcations

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Bifurcations in context of PDEs (35B32)

Related Items (17)

Non-local elliptic problem in higher dimension ⋮ Resonance phenomenon for a Gelfand-type problem ⋮ Uniform boundedness for finite Morse index solutions to supercritical semilinear elliptic equations ⋮ The Gel'fand problem for the biharmonic operator ⋮ Blow-up criteria for semilinear parabolic equations ⋮ Uniqueness and exact multiplicity results for two classes of semilinear problems ⋮ Global solution curves for self-similar equations ⋮ Morse indices and symmetry breaking for the Gelfand equation in expanding annuli ⋮ Topological instabilities in families of semilinear parabolic problems subject to nonlinear perturbations ⋮ Regularity for the fractional Gelfand problem up to dimension 7 ⋮ 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 ⋮ Regularity of extremal solutions of nonlocal elliptic systems ⋮ Global branches of non-radially symmetric solutions to a semilinear Neumann problem in a disk ⋮ Analytic imperfect bifurcation theorem and the Liouville-Gel’fand equation on a perturbed annular domain ⋮ Nonradial maximizers for a Hénon type problem and symmetry breaking bifurcations for a Liouville-Gel'fand problem with a vanishing coefficient ⋮ Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball

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• A Counterexample to the Nodal Domain Conjecture and a Related Semilinear Equation
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• Some problems in the theory of quasilinear equations
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