Article PDF
Avoid common mistakes on your manuscript.
References
Adams, R.A.: Sobolev spaces. Orlando, Academic Press 1975
Amann, H.: On the number of solutions of nonlinear equations in ordered Banach spaces. J. Funct. Anal.11, 346–384 (1972)
Amann, H.: Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces. SIAM Rev.18, 620–709 (1976)
Ancona, A.: Comparaison des mesures harmoniques et des fonctions de Green pour des opérateurs clliptiques sur un domaine lipschitzien. C.R. Acad. Sci., Paris294, 505–508 (1982)
Bandle, C.: Private communication
Barta, J.: Sur la vibration d'une membrane. C.R. Acad. Sci., Paris204, 472–473 (1937)
Berman, A., Plemmons, R.J.: Nonnegative matrices in the mathematical sciences. New York: Academic Press 1979
Bonnet, A.: Une propriété liée à la positivité pour l'opérateur biharmonique. (Preprint 1989)
Cantrell, R.S., Schmitt, K.: On the eigenvalue problem for coupled elliptic systems. SIAM J. Math. Anal.17, 850–862 (1986)
Caristi, G., Mitidieri, E.: Maximum principles for a class of non cooperative elliptic systems. Delft Prog. Rep.14, 33–56 (1990)
Caristi, G., Mitidieri, E.: Further results on maximum principles for non cooperative elliptic systems. Nonl. Ana T.M.A. (to appear)
Clément, Ph., Peletier, L.: An anti-maximum principle for second-order elliptic equations. J. Differ. Equations34, 218–229 (1979).
Clément, Ph., Peletier, L.: Positive superharmonic solutions to semi-linear elliptic eigenvalue problems. J. Math. Anal. Appl.100, 561–582 (1984).
Clément, Ph. Heijmans, H. et al.: One-parameter semigroups. Amsterdam: North-Holland 1987
Clément, Ph., Egberts, P.: On the sum of two maximal monotone operators. Differ. Integral Equations3, 1113–1124 (1990)
Cosner, C., Schaefer, P.W.: Sign-definite solutions in some linear elliptic systems. Proc. R. Soc. Edinb. (to appear)
Cosner, C.: On the complex spectra of second order elliptic systems. (Preprint)
Cranston, M., Fabes, E., Zhao, Z.: Conditional Gauge and potential theory for the Schrödinger operator. Trans. Am. Math. Soc.307, 171–194 (1988)
Cvetković, D., Doob, M., Sachs, H.: Spectra of graphs. New York London: Academic Press 1980
Falkner, N.: Feynman-Kac functionals and postive solution of 1/2 Δu+q u=0. Z. Wahrscheinlichkeitstheor. Verw. Geb.65, 19–33 (1983)
Figueiredo, D. De, Mitidieri, E.: Maximum principles for linear elliptic systems. Rend. Ist. Mat. Univ. Trieste (to appear)
Figueiredo, D. De, Mitidieri, E.: Maximum principles for cooperative elliptic system. C.R. Acad. Sci., Paris, Sér. I310, 49–52 (1990)
Gilbarg, D., Trudinger, N.S.: Elliptic partial differential equations of second order, second edition, Berlin Heidelberg New York: Springer 1983
Hess, P.: On the eigenvalue problem for weakly coupled elliptic systems. Arch. Ration. Mech. Anal.81, 151–159 (1983)
Hueber, H., Sieveking, M.: Uniform bounds for quotients of Green functions onC 1,1-domains, Ann. Inst. Fourier32, 105–117 (1982)
Hueber, H.: A uniform estimate for Green functions onC 1,1-domains. Preprint Universität Bielefeld/Forschungszentrum Bielefeld-Bochum-Stochastik
Krein, M.G., Rutman, M.A.: Linear operators leaving invariant a cone in a Banach space. Trans., I. Ser., Am. Math. Soc.10, 199–325 (1962); from Успехи Математических Наук3 (1948)
Nagel, R.: Operator matrices and reaction-diffusion equations. (Preprint 1990)
de Pagter, B.: Irreducible compact operators. Math. Z.192, 149–153 (1986)
Protter, M., Weinsberger, H.: On the spectrum of general second order operators, Bull. Am. Math. Soc.72, 251–255 (1966)
Protter, M., Weinberger, H.: Maximum principles in differential equations. Englewood Cliffs, NJ: Prentice Hall 1976
Protter, M.: The generalized spectrum of second order elliptic systems. Rocky Mt. J. Math.9, 503–518 (1979)
Schaefer, H.H.: Banach lattices and positive operators. Berlin Heidelberg New York: Springer 1974
Sweers, G.: A strong maximum principle for a noncooperative clliptic, system. SIAM J. Math. Anal.20, 367–371 (1989)
Walter, W.: A theorem on elliptic differential inequalities with an application to gradient bounds. Math. Z.200, 293–299 (1989)
Weinberger, H.F.: Some remarks on invariant sets for systems. In: Schaefer, P. (ed.) Conference on Maximum Principles and Eigenvalue Problems in P.D.E., pp. 189–207, Harlow: Longman 1987
Zhao Zhongxin: Green function, for Schrödinger operator and conditioned Feynman-Kac gauge. J. Math. Anal. Appl.116, 309–334 (1986)
Zhao Zhongxin: Green functions and conditioned gauge theorem for a 2-dimensional domain. In: Çinlar, E., et al. (eds.) Seminar on Stochastic Processes, 1987, pp. 283–294. Boston Basel Berlin, Birkhäuser 1988 Herbst, I.W., Zhao Zhongxin. Note on a 3G theorem (d=2). In: Çinlar, E., et al. (eds.) Seminar on Stochastic Processes, 1988, pp. 183–184. Boston Basel Berlin: Birkhäuser 1989
Author information
Authors and Affiliations
Additional information
This work was supported in part by N.W.O., the Netherlands Organization for Scientific Research
Rights and permissions
About this article
Cite this article
Sweers, G. Strong positivity in\(C(\bar \Omega )\) for elliptic systemsfor elliptic systems. Math Z 209, 251–271 (1992). https://doi.org/10.1007/BF02570833
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF02570833