Positive solutions of nonlinear elliptic systems
Robert Dalmasso
Annales Polonici Mathematici, Tome 58 (1993), p. 201-212 / Harvested from The Polish Digital Mathematics Library

We study the existence and nonexistence of positive solutions of nonlinear elliptic systems in an annulus with Dirichlet boundary conditions. In particular, L a priori bounds are obtained. We also study a general multiple linear eigenvalue problem on a bounded domain.

Publié le : 1993-01-01
EUDML-ID : urn:eudml:doc:262321
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     author = {Robert Dalmasso},
     title = {Positive solutions of nonlinear elliptic systems},
     journal = {Annales Polonici Mathematici},
     volume = {58},
     year = {1993},
     pages = {201-212},
     zbl = {0791.35014},
     language = {en},
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Robert Dalmasso. Positive solutions of nonlinear elliptic systems. Annales Polonici Mathematici, Tome 58 (1993) pp. 201-212. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z2p201bwm/

[000] [1] T. B. Benjamin, A unified theory of conjugate flows, Philos. Trans. Roy. Soc. 269 A (1971), 587-643. | Zbl 0226.76037

[001] [2] Ph. Clément, D. G. de Figueiredo and E. Mitidieri, Positive solutions of semilinear elliptic systems, Comm. Partial Differential Equations 17 (1992), 923-940. | Zbl 0818.35027

[002] [3] D. G. de Figueiredo, P.-L. Lions and R. D. Nussbaum, A priori estimates and existence of positive solutions of semilinear elliptic equations, J. Math. Pures Appl. 61 (1982), 41-63. | Zbl 0452.35030

[003] [4] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243. | Zbl 0425.35020

[004] [5] M. A. Krasnosel'skiĭ, Fixed points of cone-compressing and cone-extending operators, Soviet Math. Dokl. 1 (1960), 1285-1288. | Zbl 0098.30902

[005] [6] L. A. Peletier and R. C. A. M. van der Vorst, Existence and non-existence of positive solutions of non-linear elliptic systems and the biharmonic equation, Differential Integral Equations 5 (1992), 747-767. | Zbl 0758.35029

[006] [7] F. Rellich, Darstellung der Eigenwerte von Δu + λu = 0 durch ein Randintegral, Math. Z. 46 (1940), 635-636.

[007] [8] W. C. Troy, Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations 42 (1981), 400-413. | Zbl 0486.35032

[008] [9] R. C. A. M. van der Vorst, Variational identities and applications to differential systems, Arch. Rational Mech. Anal. 116 (1991), 375-398. | Zbl 0796.35059