@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}, mrnumber = {1186683}, zbl = {0785.35045}, language = {en}, url = {http://www.numdam.org/item/AIHPC_1992__9_4_367_0/} }
TY - JOUR AU - Suzuki, Takashi TI - Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity JO - Annales de l'I.H.P. Analyse non linéaire PY - 1992 SP - 367 EP - 397 VL - 9 IS - 4 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPC_1992__9_4_367_0/ LA - en ID - AIHPC_1992__9_4_367_0 ER -
%0 Journal Article %A Suzuki, Takashi %T Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity %J Annales de l'I.H.P. Analyse non linéaire %D 1992 %P 367-397 %V 9 %N 4 %I Gauthier-Villars %U http://www.numdam.org/item/AIHPC_1992__9_4_367_0/ %G en %F AIHPC_1992__9_4_367_0
Suzuki, Takashi. Global analysis for a two-dimensional elliptic eigenvalue problem with the exponential nonlinearity. Annales de l'I.H.P. Analyse non linéaire, Tome 9 (1992) no. 4, pp. 367-397. http://www.numdam.org/item/AIHPC_1992__9_4_367_0/
[1] 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] On a Differential Inequality and its Application to Geometry, Math. Z., Vol. 147, 1976, pp. 253-261. | MR | Zbl
,[3] Isoperimetric Inequalities and Applications, Pitman, Boston-London-Melboume, 1980. | MR | Zbl
,[4] Eigenfunctions and Nodal Sets, Comment. Math. Helvetici, Vol. 51, 1976, pp. 43-55. | MR | Zbl
,[5] 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
et ,[6] 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] Perturbation Theory for Linear Operators, 2nd ed., Springer, Berlin-Heidelberg- New York, 1976. | MR | Zbl
,[8] Positive Solutions of Convex Nonlinear Eigenvalue Problem, J. Diff. Eq., Vol. 16, 1974, pp. 103-125. | MR | Zbl
et ,[9] Some Positive Problems Suggested by Nonlinear Heat Generation, J. Math. Mech., 16, 1967, pp. 1361-1376. | MR | Zbl
et ,[10] On the Number of Boundary Value Problems with Convex Nonlinearities, J. Math. Anal. Appl., Vol. 35, 1971, pp. 389-404. | MR | Zbl
,[11] On Non-Radially Symmetric Bifurcations in the Annulus, J. Diff. Eq., 80, 1989, pp. 251-279. | MR | Zbl
,[12] Sur l'équation aux différences partielles ∂2 Log λ/∂u∂v±λ/2a2=0, J. Math., Vol. 18, 1853, pp. 71-72.
,[13] A Two-Dimensional Dirichlet Problem with an Exponential Nonlinearily, SIAM J. Math. Anal., Vol. 14, 1983, pp. 934-946. | MR | Zbl
,[14] 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
et ,[15] Asymptotic Analysis for Two-Dimensional Elliptic Eigenvalue Problems with Exponentially-Dominated Nonlinearities, Asymptotic Analysis, Vol. 3, 1990, pp. 173-188. | MR | Zbl
et ,[16] On the Principal Frequency of a Membrane, Pac. J. Math., Vol. 8, 1958, pp. 285-293. | MR | Zbl
,[17] Remarks on Courant's Nodal Line Theorem, Comm. Pure Appl. Math., Vol. 9, 1956, pp. 543-550. | MR | Zbl
,[18] On the Nonlinear Eigenvalue Problem Δu+λeu=0, Trans. Am. Math. Soc., Vol. 309, 1988, pp. 591-608. | MR | Zbl
et ,[19] Counterexample to a Conjecture of H. Hopf, Pacific J. Math., Vol. 121, 1986, pp. 193-243. | MR | Zbl
,[20] 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
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