Positive solutions of nonlinear elliptic systems

Robert Dalmasso

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 201-212
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Robert Dalmasso. "Positive solutions of nonlinear elliptic systems." Annales Polonici Mathematici 58.2 (1993): 201-212. <http://eudml.org/doc/262321>.

@article{RobertDalmasso1993,
abstract = {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.},
author = {Robert Dalmasso},
journal = {Annales Polonici Mathematici},
keywords = {a priori bounds; nonlinear elliptic systems; Maximum Principle; semilinear elliptic systems in an annulus; homogeneous Dirichlet conditions; maximum principle; positive solutions; a priori bounds; multiple linear eigenvalue problem},
language = {eng},
number = {2},
pages = {201-212},
title = {Positive solutions of nonlinear elliptic systems},
url = {http://eudml.org/doc/262321},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Robert Dalmasso
TI - Positive solutions of nonlinear elliptic systems
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 201
EP - 212
AB - 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.
LA - eng
KW - a priori bounds; nonlinear elliptic systems; Maximum Principle; semilinear elliptic systems in an annulus; homogeneous Dirichlet conditions; maximum principle; positive solutions; a priori bounds; multiple linear eigenvalue problem
UR - http://eudml.org/doc/262321
ER -

References

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  3. [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. Zbl0452.35030
  4. [4] B. Gidas, W.-M. Ni and L. Nirenberg, Symmetry and related properties via the maximum principle, Comm. Math. Phys. 68 (1979), 209-243. Zbl0425.35020
  5. [5] M. A. Krasnosel'skiĭ, Fixed points of cone-compressing and cone-extending operators, Soviet Math. Dokl. 1 (1960), 1285-1288. Zbl0098.30902
  6. [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. Zbl0758.35029
  7. [7] F. Rellich, Darstellung der Eigenwerte von Δu + λu = 0 durch ein Randintegral, Math. Z. 46 (1940), 635-636. 
  8. [8] W. C. Troy, Symmetry properties in systems of semilinear elliptic equations, J. Differential Equations 42 (1981), 400-413. Zbl0486.35032
  9. [9] R. C. A. M. van der Vorst, Variational identities and applications to differential systems, Arch. Rational Mech. Anal. 116 (1991), 375-398. Zbl0796.35059

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