On the nonlinear eigenvalue problem $\Delta u+\lambda e^ u=0$
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- by Takashi Suzuki and Ken’ichi Nagasaki PDF
- Trans. Amer. Math. Soc. 309 (1988), 591-608 Request permission
Abstract:
The structure of the set $\mathcal {C}$ of solutions of the nonlinear eigenvalue problem $\Delta u + \lambda {e^u} = 0$ under Dirichlet condition in a simply connected bounded domain $\Omega$ is studied. Through the idea of parametrizing the solutions $(u, \lambda )$ in terms of $s = \lambda \int _\Omega {{e^u} dx}$, some profile of $\mathcal {C}$ is illustrated when $\Omega$ is star-shaped. Finally, the connectivity of the branch of Weston-Moseley’s large solutions to that of minimal ones is discussed.References
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Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 309 (1988), 591-608
- MSC: Primary 35J65; Secondary 35P30, 47H12, 47H15
- DOI: https://doi.org/10.1090/S0002-9947-1988-0961602-6
- MathSciNet review: 961602