Almost periodic upper and lower solutions

Journal of Differential Equations

Volumn 193, Issue 2, 2003, Pages 343-358

  Ortega, Rafael ^a   Tarallo, Massimo ^b  

^a UNIVERSITY OF GRANADA   (Spain)

^b Dipartimento di Matematica dell'Universita   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042854712     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-0396(03)00130-X     Document Type: Article

References (17)

1. E.A. Coddington, N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
2. C. De Coster, P. Habets, Upper and lower solutions in the theory of ODE boundary value problems: classical and recent results, in: Nonlinear Analysis and Boundary Value Problems for Ordinary Differential Equations, CISM Courses, Vol. No. 371, Springer, Wien, 1996, pp. 1-78.
3. A.M. Fink, Almost Periodic Differential Equations, in: Lecture Notes in Mathematics, Vol. 377, Springer, Berlin, 1974.
4. A.M. Fink, P. Frederickson, Ultimate boundedness does not imply almost periodicity, J. Differential Equations 9 (1971) 280-284.
5. R.A. Johnson, Minimal functions with unbounded integral, Israel Math. J. 31 (1978) 133-141.
6. R.A. Johnson, A linear almost periodic equation with an almost automorphic solution, Proc. Amer. Math. Soc. 82 (1981) 199-205.
7. A. Katok, B. Hasselblatt, Introduction to the Modern Theory of Dynamical Systems, Cambridge University Press, Cambridge, 1995.
8. H.W. Knobloch, Comparison theorems for nonlinear second order differential equations, J. Differential Equations 1 (1965) 1-26.
9. N.G. Markley, Homeomorphisms of the circle without periodic points, Proc. London Math. Soc. 20 (1970) 688-698.
10. M. Nagumo, On principally linear elliptic differential equations of the second order, Osaka Math. J. 6 (1954) 207-229.
11. V.V. Nemytskii, V.V. Stepanov, Qualitative Theory of Differential Equations, Princenton University Press, Princenton, 1960.
12. Z. Opial, Sur une équation différentielle presque-périodique sans solution presque-périodique, Bull. Acad. Polon. Sci. Ser. Math. Astr. Phys. IX (1961) 673-676.
13. R. Ortega, M. Tarallo, Massera's theorem for quasi-periodic differential equations, Topological Methods Nonlinear Anal. 19 (2002) 39-62.
14. R. Ortega, M. Tarallo, Almost periodic linear differential equations with non-separated solutions, to appear, www.ugr.es/~ecuadif/fuentenueva.htm.
15. K. Schmitt, Periodic solutions of nonlinear second order differential equations, Math. Z. 98 (1967) 200-207.
16. K. Schmitt, J. Ward, Almost periodic solutions of nonlinear second order differential equations, Results Math. 21 (1992) 190-199.
17. V.V. Zhikov, B.M. Levitan, Favard theory, Russian Math. Surveys 32 (1977) 129-180.