This is a preview of subscription content, log in via an institution to check access.
References
S.W. Ali, “Steady states in the diffusive Volterra-Lotka model for several competing species,” Dissertation, University of Miami, 1986.
H. Amann, “Fixed point equations and nonlinear eigenvalue problems in ordered Banach spaces,” SIAM Review 18 (1976), 620–709.
J. Barta, “Sur la vibration fondamentale d’une membrane,” C.R. Acad. Sci. Paris 204 (1937), 472–473.
R.S. Cantrell and C. Cosner, “On the uniqueness and stability of positive solutions in the Lotka-Volterra competition model with diffusion,” to appear, Houston J. of Math.
R.S. Cantrell and K. Schmitt, “On the eigenvalue problem for coupled elliptic systems,” SIAM J. Math. Anal. 17 (1986), 850–862.
C. Cosner and M.H. Protter, “Bounds for the spectrum and the norm of solutions of nonlinear elliptic equations and systems,” J. Differential Equations 56 (1985), 270–289.
J.-P. Gossez and E. Lami Dozo, “On the principal eigenvalue of a second order linear elliptic problem”,Arch. Rat. Mech. Anal. 89 (1985), 169–176.
P. Hess, “On the eigenvalue problem for weakly-coupled elliptic systems,” Arch. Rat. Mech. Anal. 81 (1983), 151–159.
P. Hess and T. Kato, “On some linear and nonlinear eigenvalue problems with indefinite weight function,” Comm. Partial Differential Equations 5 (1980), 999–1030.
W.W. Hooker, “Lower bounds for the first eigenvalue of elliptic equations of orders two and four,” Tech. Rep. 10 AF 49 (638)-398, Univ. of California, Berkeley, California 1960.
T. Kato, “Schrödinger operators with singular potentials,” Israel J. Math 13 (1972), 135–148.
C.B. Morrey, Jr., Multiple Integrals in the Calculus of Variations, Springer-Verlag, New York, 1966.
R. Nussbaum, “Positive operators and elliptic eigenvalue problems,” Math. Z. 186 (1984), 247–264.
H. Ogawa and M.H. Protter, “A lower bound for the first eigenvalue of second order elliptic operators,” Proc. Amer. Math. Soc. 19 (1968), 292–295.
M.H. Protter, “Lower bounds for the first eigenvalue of elliptic equations,” Ann. of Math. 71 (1960), 423–444.
M.H. Protter, “The generalized spectrum of second order elliptic systems,” Rocky Mountain J. Math. 9 (1979), 503–518.
M.H. Protter and H.F. Weinberger, “On the spectrum of general second order elliptic operators,” Bull. Amer. Math. Soc. 72 (1966), 251–255.
M.H. Protter and H.F. Weinberger, Maximum Principles in Differential Equations, Prentice Hall, Englewood Cliffs, New Jersey, 1967.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cosner, C. On the complex spectra of second order elliptic systems. Results. Math. 15, 15–34 (1989). https://doi.org/10.1007/BF03322444
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF03322444