Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity
Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 4, pp. 367-397.
@article{AIHPC_1992__9_4_367_0,
     author = {Suzuki, Takashi},
     title = {Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {367--397},
     publisher = {Gauthier-Villars},
     volume = {9},
     number = {4},
     year = {1992},
     zbl = {0785.35045},
     mrnumber = {1186683},
     language = {en},
     url = {http://archive.numdam.org/item/AIHPC_1992__9_4_367_0/}
}
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Suzuki, Takashi. Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Volume 9 (1992) no. 4, pp. 367-397. http://archive.numdam.org/item/AIHPC_1992__9_4_367_0/

[1] C. Bandle, Existence Theorems, Qualitative Results and a priori Bounds for a Class of Nonlinear Dirichlet Problems, Arch. Rat. Mech. Anal., Vol. 58, 1975, pp. 219-238. | MR | Zbl

[2] C. Bandle, On a Differential Inequality and its Application to Geometry, Math. Z., Vol. 147, 1976, pp. 253-261. | MR | Zbl

[3] C. Bandle, Isoperimetric Inequalities and Applications, Pitman, Boston-London-Melboume, 1980. | MR | Zbl

[4] S.Y. Cheng, Eigenfunctions and Nodal Sets, Comment. Math. Helvetici, Vol. 51, 1976, pp. 43-55. | MR | Zbl

[5] M.G. Crandall et P.H. Rabinowitz, Some Continuation and Variational Methods for Positive Solutions of Nonlinear Elliptic Eigenvalu Problems, Arch. Rat. Mech. Anam., Vol. 58, 1975, pp. 207-218. | MR | Zbl

[6] H. Fujita, On the Nonlinear Equations Δu+eu=0 and ∂v/∂t = Δv + ev, Bull. Am. Math. Soc., Vol. 75, 1969, pp. 132-135. | MR | Zbl

[7] T. Kato, Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin-Heidelberg- New York, 1976. | MR | Zbl

[8] J.P. Keener et H.B. Keller, Positive Solutions of Convex Nonlinear Eigenvalue Problem, J. Diff. Eq., Vol. 16, 1974, pp. 103-125. | MR | Zbl

[9] H.B. Keller et D.S. Cohen, Some Positive Problems Suggested by Nonlinear Heat Generation, J. Math. Mech., 16, 1967, pp. 1361-1376. | MR | Zbl

[10] T. Laetsch, On the Number of Boundary Value Problems with Convex Nonlinearities, J. Math. Anal. Appl., Vol. 35, 1971, pp. 389-404. | MR | Zbl

[11] S.S. Lin, On Non-Radially Symmetric Bifurcations in the Annulus, J. Diff. Eq., 80, 1989, pp. 251-279. | MR | Zbl

[12] J. Liouville, Sur l'équation aux différences partielles ∂2 Log λ/∂u∂v±λ/2a2=0, J. Math., Vol. 18, 1853, pp. 71-72.

[13] J.L. Moseley, A Two-Dimensional Dirichlet Problem with an Exponential Nonlinearily, SIAM J. Math. Anal., Vol. 14, 1983, pp. 934-946. | MR | Zbl

[14] K. Nagasaki et T. Suzuki, Radial and Nonradial Solutions for the Nonlinear Eigenvalue problem Δu+λeu=0 on Annului in R2, J. Diff. Eq., Vol. 87, 1990, pp. 144-168. | MR | Zbl

[15] K. Nagasaki et T. Suzuki, Asymptotic Analysis for Two-Dimensional Elliptic Eigenvalue Problems with Exponentially-Dominated Nonlinearities, Asymptotic Analysis, Vol. 3, 1990, pp. 173-188. | MR | Zbl

[16] Z. Nehari, On the Principal Frequency of a Membrane, Pac. J. Math., Vol. 8, 1958, pp. 285-293. | MR | Zbl

[17] Å. Pleijel, Remarks on Courant's Nodal Line Theorem, Comm. Pure Appl. Math., Vol. 9, 1956, pp. 543-550. | MR | Zbl

[18] T. Suzuki et K. Nagasaki, On the Nonlinear Eigenvalue Problem Δu+λeu=0, Trans. Am. Math. Soc., Vol. 309, 1988, pp. 591-608. | MR | Zbl

[19] H. Wente, Counterexample to a Conjecture of H. Hopf, Pacific J. Math., Vol. 121, 1986, pp. 193-243. | MR | Zbl

[20] V.H. Weston, On the Asymptotic Solution of a Partial Differential Equation with an Exponential Nonlinearity, SIAM J. Math. Anal., Vol. 9, 1978, pp. 1030-1053. | MR | Zbl