286
where (3*(s) := E[-T]~j~O (3(s + j) for s E [-1,0] with [-T] := sup{k E Z : k ::;
-T} and f3I(-oo.-T)= O. We refer to [Hetzer (1995)J for details.
REFERENCES
Amann H (1976) Fixed point equations and nonlinear eigenvalue problems in ordered
Banach spaces. Siam Review 45:620-709
Amann H (1983) Dual semigroups and second order linear elliptic differential equations.
Israel J. Math. 45:225-254
Amann H (1984) Existence and regularity for semilinear parabolic evolution equations.
Ann. Scuola Norm. Sup. Pisa 11:593-676
Amann H (1990) Ordinary differential equations: an introduction to nonlinear analysis.
de Gruyter, Berlin, New York
Amann H (1993) Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems in Function Spaces, Differential Operators and Nonlinear Analysis, Schmeisser H. D., Triebel H. {eds.}. Teubner-Texte zur Mathematik 133:9-126
Bhattacharya K, Ghil M, Vulis IL (1982) Internal variability of an energy balance climate
model. J. Atmosph. Sci. 39:1747-1773
Budyko MI (1969) The effect of solar radiation variations on the climate of the earth.
Tellus 21:611-619
Daners D, Koch Medina P (1993) Abstract evolution equations, periodic problems and
applications. Pitman Research Notes in Mathematics vol. 78
Diaz IJ (1995), this volume
Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: atmospheric dynamics,
dynamo theory, and climate dynamics. Springer-Verlag New York
Hale JK (1988) Asymptotic Behavior of Dissipative Systems. American Mathematical
Society, Providence
Henderson-Sellers A, McGuffie K (1987) A Climate Modelling Primer.John Wiley and
Sons Chichester
Hess P (1991) Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics vol 247
Hess P, Polacik P (1993) Boundedness of prime periods of stable cycles and convergence
to fixed points in discrete monotone dynamical systems. SIAM Journ. Math. Anal.
24:1312-1330
Hetzer G (1990) The structure of the principal component for semilinear diffusion equations from energy balance climate models. Houston J. Math. 16:203-216
Hetzer G (1994) A parameter dependent time-periodic reaction-diffusion equation from
climate modeling: S-shapedness of the principal branch of fixed points of the timeI-map. Differential and Integral Equations 7:1419-1425
Hetzer G (1995) A functional reaction-diffusion equation from climate modeling: Sshapedness of the principal branch. Diff. and Integral Eq., to appear
Hetzer G, Jarausch H, Mackens W (1989) A multiparameter sensitivity analysis of a 2D
diffusive climate model. Impact Comput. Sci. Eng. 1:327-393
Hetzer G, Schmidt PL (1990) A global attractor and stationary solutions for a reaction diffusion system arising from climate modeling. Nonlinear Analysis: Theory,
Methods, and Appl. 14:915-926
where (3*(s) := E[-T]~j~O (3(s + j) for s E [-1,0] with [-T] := sup{k E Z : k ::;
-T} and f3I(-oo.-T)= O. We refer to [Hetzer (1995)J for details.
REFERENCES
Amann H (1976) Fixed point equations and nonlinear eigenvalue problems in ordered
Banach spaces. Siam Review 45:620-709
Amann H (1983) Dual semigroups and second order linear elliptic differential equations.
Israel J. Math. 45:225-254
Amann H (1984) Existence and regularity for semilinear parabolic evolution equations.
Ann. Scuola Norm. Sup. Pisa 11:593-676
Amann H (1990) Ordinary differential equations: an introduction to nonlinear analysis.
de Gruyter, Berlin, New York
Amann H (1993) Nonhomogeneous linear and quasilinear elliptic and parabolic boundary value problems in Function Spaces, Differential Operators and Nonlinear Analysis, Schmeisser H. D., Triebel H. {eds.}. Teubner-Texte zur Mathematik 133:9-126
Bhattacharya K, Ghil M, Vulis IL (1982) Internal variability of an energy balance climate
model. J. Atmosph. Sci. 39:1747-1773
Budyko MI (1969) The effect of solar radiation variations on the climate of the earth.
Tellus 21:611-619
Daners D, Koch Medina P (1993) Abstract evolution equations, periodic problems and
applications. Pitman Research Notes in Mathematics vol. 78
Diaz IJ (1995), this volume
Ghil M, Childress S (1987) Topics in geophysical fluid dynamics: atmospheric dynamics,
dynamo theory, and climate dynamics. Springer-Verlag New York
Hale JK (1988) Asymptotic Behavior of Dissipative Systems. American Mathematical
Society, Providence
Henderson-Sellers A, McGuffie K (1987) A Climate Modelling Primer.John Wiley and
Sons Chichester
Hess P (1991) Periodic-parabolic boundary value problems and positivity. Pitman Research Notes in Mathematics vol 247
Hess P, Polacik P (1993) Boundedness of prime periods of stable cycles and convergence
to fixed points in discrete monotone dynamical systems. SIAM Journ. Math. Anal.
24:1312-1330
Hetzer G (1990) The structure of the principal component for semilinear diffusion equations from energy balance climate models. Houston J. Math. 16:203-216
Hetzer G (1994) A parameter dependent time-periodic reaction-diffusion equation from
climate modeling: S-shapedness of the principal branch of fixed points of the timeI-map. Differential and Integral Equations 7:1419-1425
Hetzer G (1995) A functional reaction-diffusion equation from climate modeling: Sshapedness of the principal branch. Diff. and Integral Eq., to appear
Hetzer G, Jarausch H, Mackens W (1989) A multiparameter sensitivity analysis of a 2D
diffusive climate model. Impact Comput. Sci. Eng. 1:327-393
Hetzer G, Schmidt PL (1990) A global attractor and stationary solutions for a reaction diffusion system arising from climate modeling. Nonlinear Analysis: Theory,
Methods, and Appl. 14:915-926