On a class of nonlinear elliptic equations

M. Chipot

ArticleOriginal scientific text

Title

On a class of nonlinear elliptic equations

Authors ¹

Affiliations

Département de Mathématiques et Informatique, Université de Metz, Ile du Saulcy, F-57045 Metz Cedex 01, France

[AW] L. Alfonsi and F. B. Weissler, Blow up in $ℝ^{n}$ for a parabolic equation with a damping nonlinear gradient term, preprint.
[CV] M. Chipot and F. Voirol, in preparation.
[CW₁] M. Chipot and F. B. Weissler, Some blow up results for a nonlinear parabolic equation with a gradient term, SIAM J. Math. Anal. 20 (4) (1989), 886-907.
[CW₂] M. Chipot and F. B. Weissler, Nonlinear Diffusion Equations and Their Equilibrium States, Math. Sci. Res. Inst. Publ. 12, Vol. 1, Springer, 1988.
[F] M. Fila, Remarks on blow up for a nonlinear parabolic equation with a gradient term, Proc. Amer. Math. Soc. 111 (1991), 795-801.
[KP] B. Kawohl and L. A. Peletier, Observations on blow up and dead cores for nonlinear parabolic equations, Math. Z. 202 (1989), 207-217.
[GNN] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243.
[GT] D. Gilbarg and N. S. Trudinger, Elliptic Partial Differential Equations of Second Order, Springer, 1985.
[P₁] S. I. Pokhozhaev, Solvability of an elliptic problem in $ℝ^{N}$ with supercritical nonlinearity exponent, Dokl. Akad. Nauk SSSR 313 (6) (1990), 1356-1360 (in Russian).
[P₂] S. I. Pokhozhaev, Positivity classes of elliptic operators in $ℝ^{N}$ with supercritical nonlinearity exponent, ibid. 314 (1990), 558-561 (in Russian).
[Q] P. Quittner, Blow up for semilinear parabolic equations with a gradient term, preprint.
[V] F. Voirol, Thesis, University of Metz, in preparation.
[W] F. B. Weissler, private communication.

Title

On a class of nonlinear elliptic equations

Affiliations

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