A Granas type approach to some continuation theorems and periodic boundary value problems with impulse

[1] A. Capietto, J. Mawhin and F. Zanolin, A continuation approach to superlinear periodic boundary value problems, J. Differential Equations 88 (1990), 347–395.
[2] , Boundary value problems for forced superlinear second order ordinary differential equations, SISSA Ref. 106/92/M (1992), 1–10.
[3] K. Deimling, Nonlinear Functional Analysis, Springer-Verlag, Berlin, 1985.
[4] L. Erbe and W. Krawcewicz, Existence of solutions to boundary value problems for impulsive second order differential inclusions, Rocky Mountain J. Math. 22 (1992), 519–540.
[5] M. Frigon, Application de la theorie de la transversalite topologique a des problemes non lineaires pour des equations differentielles ordinaires, Dissertationes Math. 296 (1990).
[6] A. Granas, Homotopy extension theorem in Banach spaces and some of its applications to the theory of non-linear equations, Bull. Acad. Polon. Sci. 7 (1959), 387–394.
[7] A. Granas, R. Guenther and J. Lee, Nonlinear boundary value problems for ordinary differential equations, Dissertationes Math. 244 (1985).
[8] W. Krawcewicz, Contribution a la theorie des equations non lineaires dans les espaces de Banach, Dissertationes Math. 273 (1988).
[9] J. Leray et J. Schauder, Topologie et equations fonctionnelles, Ann. Sci. Ecole Norm. Sup. (3) 51 (1934), 45–78.
[10] D. O’Regan, Second and higher order systems of boundary value problems, J. Math. Anal. Appl. 156 (1991), 120–149.
[11] R. Precup, Generalized topological transversality and existence theorems, Libertas Math. 11 (1991), 65–79.
[12] , On the topological transversality principle, Nonlinear Anal. 20 (1993), 1–9.
[13] H. Schaefer, Uber die Methode der a priori Schranken , Math. Ann. 129 (1955), 415– 416.
[14] R. Schoneberg, Leray-Schauder principles for condensing multivalued mappings in topological linear spaces, Proc. Amer. Math. Soc. 72 (1978), 268–270.