This is a preview of subscription content, log in via an institution to check access.
References
I. Bernstein andA. Halanay, The index of a critical point and the existence of periodic solutions to a system with small parameter. Dokl. Akad. Nauk. SSSR111, 923–925 (1956).
E. N. Dancer, Boundary value problems for weakly nonlinear ordinary differential equations. Bull. Austral. Math. Soc.15, 321–328 (1976).
D. De Figueiredo andJ. P. Gossez, Nonresonance below the first eigenvalue for a semilinear elliptic problem. Math. Ann.281, 589–610 (1988).
T. Ding, R. Iannacci andF. Zanolin, On periodic solutions of sublinear Duffing equations. J. Math. Anal. Appl.158, 316–322 (1991).
T.Ding, R.Iannacci and F.Zanolin, Existence and multiplicity results for periodic solutions of semilinear Duffing equations. J. Differential Equations, to appear.
M. L. Fernandes andF. Zanolin, Periodic solutions of a second order differential equation with one-sided growth restrictions on the restoring term. Arch. Math.51, 151–163 (1988).
M. L. Fernandes, P. Omari andF. Zanolin, On the solvability of a semilinear two-point BVP around the first eigenvalue. Differential Integral Equations2, 63–79 (1989).
S.Fucik, Solvability of Nonlinear Equations and Boundary Value Problems. Dordrecht, 1980.
R.Gaines and J.Mawhin, Coincidence Degree and Nonlinear Differential Equations. LNM568, Berlin-Heidelberg-New York 1977.
R. E. Gomory, Critical points at infinity and forced oscillations. In: Contributions to the theory of nonlinear oscillations, vol. 3. Ann. of Math. Stud.36, 85–126 (1956).
M. A.Krasnosel'skii, The operator of Translation along Trajectories of Differential Equations. Providence, R.I. 1968.
M. A. Krasnosel'skii andA. L. Perov, Existence of solutions for certain nonlinear operator equations. Dokl. Akad. Nauk. SSSR126, 15–18 (1959).
M. A.Krasnosel'skii, A. I.Perov, A. I.Povolockii and P. P.Zabreiko, Plane Vector Fields. New York 1966.
J.Mawhin, Nonlinear variational two-point boundary value problems. In: Proceedings of the conference “Variational Methods”. Paris 1988, H. Beresticki, J.-H. Coron, I. Ekeland; ed., 209–219, Basel-Boston 1990.
J. Mawhin andJ. R. Ward, Periodic solutions of some forced Lienard differential equations at resonance. Arch. Math.41, 337–351 (1983).
J.Mawhin and M.Willem, Critical Point Theory and Hamiltonian Systems. Berlin-Heidelberg-New York 1989.
P. Omari, G. Villari andF. Zanolin, Periodic solutions of the Lienard equation with one-sided growth restrictions. J. Differential Equations67, 278–293 (1987).
Z. Opial, Sur les solutions periodiques de l'equation differentiellex″+g(x)=p(t). Bull. Acad. Polon. Sci. Sér. Sci. Math., Astronom. Phys.8, 151–156 (1960).
Z. Opial, Sur les periodes des solutions de l'equation differentiellex″+g(x)=0. Ann. Polon. Math.10, 49–72 (1961).
Z. Opial, Sur l'existence des solutions periodiques de l'equation differentiellex″ + f(x,x′)x′ + g(x) = p(t). Ann. Polon. Math.11, 149–159 (1961).
R. Reissig, Periodic solutions of a second order differential equation including a one-sided restoring term. Arch. Math.33, 85–90 (1979).
R. Reissig, G. Sansone undR. Conti, Qualitative Theorie Nichtlinearer Differentialgleichungen. Cremonese, Roma 1963.
K. Schmitt, Periodic solutions of a forced nonlinear oscillator involving a one-sided restoring force. Arch. Math.31, 70–73 (1978).
J. R. Ward, Periodic solutions for systems of second order ordinary differential equations. J. Math. Anal. Appl.81, 92–98 (1981).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fonda, A., Zanolin, F. On the use of time-maps for the solvability of nonlinear boundary value problems. Arch. Math 59, 245–259 (1992). https://doi.org/10.1007/BF01197322
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01197322