RENDICONTI DEL SEMINARIO MATEMATICO

154 D. Papini - F. Zanolinavailable all the tools which are needed in order to achieve a full extension of thetopological results contained in [59, 60] and partially recalled in Section 1.2, to mapswhich expand the arcs along one direction. A more complete investigation on thissubject will appear in a future work.5. AcknowledgmentF. Zanolin gratefully thanks professor Gaetano Zampieri and professor Hisao FujitaYashima for the kind invitation.References[1] ALEXANDER J.C., A primer on connectivity, in: “Fixed point theory, Proc. Conf., Sherbrooke/Can.1980”, (Eds. Fadell E. and Fournier G.), Lect. Notes Math. 886, Springer - Verlag, Berlin New York1981, 455–483.[2] ANDRES J., GAUDENZI M. AND ZANOLIN F., A transformation theorem for periodic solutions ofnondissipative systems, Rend. Sem. Mat. Univ. Pol. Torino 48 (1990), 171–186 (1992).[3] ANDRES J., GÓRNIEWICZ L. AND LEWICKA M., Partially dissipative periodic processes, in: “Topologyin nonlinear analysis (Warsaw 1994)”, Banach Center Publ. 35, Polish Acad. Sci., Warsaw 1996,109–118.[4] BONHEURE D., GOMES J.M. AND HABETS P., Multiple positive solutions of superlinear ellipticproblems with sign-changing weight, J. Differential Equations 214 (2005), 36–64.[5] BUTLER G.J., Oscillation theorems for a nonlinear analogue of Hill’s equation, Quart. J. Math. Oxford,Ser. 27 (2) (1976), 159–171.[6] BUTLER G.J., Rapid oscillation, nonextendability, and the existence of periodic solutions to secondorder nonlinear differential equations, J. Differential Equations 22 (1976), 467–477.[7] CAPIETTO A., Continuation results for operator equations in metric ANRs, Boll. Unione Mat. Ital.,VII. Ser. B 8 (1994), 135–150.[8] CAPIETTO A., DAMBROSIO W. AND PAPINI D., Superlinear indefinite equations on the real line andchaotic dynamics, J. Differential Equations 181 (2002), 419–438.[9] CAPIETTO A., HENRARD M., MAWHIN J. AND ZANOLIN F., A continuation approach to some forcedsuperlinear Sturm-Liouville boundary value problems, Topol. Methods Nonlinear Anal. 3 (1994), 81–100.[10] CAPIETTO A., MAWHIN J. AND ZANOLIN F., A continuation approach to superlinear periodic boundaryvalue problems, J. Differential Equations 88 (1990), 347–395.[11] CONLEY C., An application of Wazewski’s method to a non–linear boundary value problem whicharises in population genetics, J. Math. Biol. 2 (1975), 241–249.[12] COVOLAN D., Dinamiche di tipo caotico: un approccio topologico, Tesi di laurea magistrale, Universitàdi Udine, Udine 2005.[13] DALBONO F. AND ZANOLIN F., Multiplicity results for asymptotically linear equations, using therotation number approach, to appear on Med. J. Math.[14] DAMBROSIO W. AND PAPINI D., Periodic solutions of asymptotically linear second order equationswith indefinite weight, Ann. Mat. Pura Appl. 183 (2004), 537–554.[15] DEIMLING K., Nonlinear functional analysis, Springer-Verlag, Berlin–Heidelberg 1985.[16] DUGUNDJI J. AND GRANAS A., Fixed point theory. I, Monografie Matematyczne [MathematicalMonographs] 61, Państwowe Wydawnictwo Naukowe (PWN), Warsaw 1982.[17] EASTON R.W., Isolating blocks and symbolic dynamics, J. Differential Equations 17 (1975), 96–118.