Radial solutions for \(\Delta{}u+\lambda{}e^ u=0\) on annuli in higher dimensions

DOI10.1016/0022-0396(92)90129-BzbMath0776.35047OpenAlexW1997244845MaRDI QIDQ1201114

Ken'ichi Nagasaki, Takashi Suzuki

Publication date: 17 January 1993

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-0396(92)90129-b

zbMATH Keywords

bifurcation diagramEmden-Fowler equationradial solutionexponential nonlinearityphase space analysis

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Topological structure of integral curves, singular points, limit cycles of ordinary differential equations (34C05)

Related Items (8)

Spectral and related properties about the Emden-Fowler equation \(-\Delta u=\lambda e^ u\) on circular domains ⋮ Non-local elliptic problem in higher dimension ⋮ Analysis of boundary bubbling solutions for an anisotropic Emden-Fowler equation ⋮ On the existence of bounded positive solutions for a class of singular BVPs ⋮ Morse indices and symmetry breaking for the Gelfand equation in expanding annuli ⋮ Global bifurcations of solutions of Emden-Fowler-type equation \(-\Delta u(x)=\lambda f(u(x))\) on an annulus in \({\mathbb R}^n\), \(n\geq 3\) ⋮ On the existence of positive radial solutions for a certain class of elliptic BVPs ⋮ Fixed point and variational methods for certain classes of boundary-value problems

Cites Work

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• On the existence of positive radial solutions for nonlinear elliptic equations in annular domains
• Positive radial solutions and non-radial bifurcation for semilinear elliptic equations in annular domains
• Symmetry and related properties via the maximum principle
• A priori estimates and existence of positive solutions of semilinear elliptic equations
• Some continuation and variational methods for positive solutions of nonlinear elliptic eigenvalue problems
• On non-radially symmetric bifurcation in the annulus
• Nonlinear elliptic problems in annular domains
• Quasilinear Dirichlet problems driven by positive sources
• Radial and nonradial solutions for the nonlinear eigenvalue problem \(\Delta u+\lambda e^ u=0\) on annuli in \({\mathbb{R}}^ 2\)
• Some problems in the theory of quasilinear equations

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