Esistenza e unicità degli stati fondamentali per equazioni ellittiche quasilineari

Franchi, Bruno ; Lanconelli, Ermanno ; Serrin, James

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti, Tome 78 (1985), p. 121-126 / Harvested from Biblioteca Digitale Italiana di Matematica

Résumé

In this paper we describe some existence and uniqueness theorems for radial ground states of a class of quasilinear elliptic equations. In particular, the mean curvature operator and the degenerate Laplace operator are considered.

Détail

Publié le : 1985-11-01

MR 0944381 | Zbl 0647.35025

Bibliographie

[BL] Berestycki, H. e Lions, P.L. (1983) - Nonlinear Scalar Field equations, I, «Arch. Rational Mech. Anal.», 82, 313-345. | MR 695535 | Zbl 0533.35029

[BLP] Berestycki, H., Lions, P.L. e Peletier, L.A. (1981) - An ODE Approach to the Existence of Positive Solutions for Semilinear Problems in $\mathbb{R}^{n}$, «Indiana Univ. Math. J.», 30, 141-157. | MR 600039 | Zbl 0522.35036

[C] Citti, G. (1985) - Positive Solutions for a Quasilinear Degenerate Elliptic Equation in $\mathbb{R}^{n}$, Preprint. | MR 929619 | Zbl 0659.35039

[FLS] Franchi, B., Lanconelli, E. e Serrin, J. (1985) - Existence and Uniqueness of Positive Solution of Quasilinear Equations in $\mathbb{R}^{n}$, to appear. | MR 1378680 | Zbl 0853.35035

[GNN] Gidas, B., Ni, W.M. e Nirenberg, L. (1981) - Symmetry of Positive Solutions of Nonlinear Elliptic Equations in $\mathbb{R}^{n}$, «Advances in Math. Studies», 7 A, 369-402 | MR 634248 | Zbl 0469.35052

[PS1] Peletier, L.A. e Serrin, J. (1983) - Uniqueness of Positive Solutions of Semilinear Equations in $\mathbb{R}^{n}$, «Arch. Rational Mech. Anal.», 81, 181-197. | MR 682268 | Zbl 0516.35031

[PS2] Peletier, L.A. e Serrin, J. (1986) - Uniqueness of Nonnegative Solutions of Semilinear Equations in $\mathbb{R}^{n}$, «J. of Diff. Eq.», 61, 380-397. | MR 829369 | Zbl 0577.35035