An Abstract Existence Theorem at Resonance and Its Applications

Journal of Differential Equations

Volumn 145, Issue 2, 1998, Pages 274-294

  Ma, Shiwang ^a   Wang, Zhicheng ^a   Yu, Jianshe ^a  

^a HUNAN UNIVERSITY   (China)

Author keywords

Brouwer degree; coincidence degree; resonance; operater equation; periodic solution; semilinear equation

Indexed keywords

EID: 0000317073     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.1997.3397     Document Type: Article

References (17)

1. Hale J. K. Ordinary Differential Equations. 1969;Wiley-Interscience, New York.
2. Nagle R. K. Nonlinear boundary value problems for ordinary differential equations with a small parameter. SIAM J. Math. Anal. 9:1978;719-729.
3. Cesari L., Kannan R. Solutions in large of lienard systems with forcing term. Ann. Mat. Pura Appl. 111:1976;101-124.
4. Rouche N., Mawhin J. Ordinary Differential Equations. 1980;Pitman, London.
5. Fucik S. Solvability of Nonlinear Equations and Boundary Value Problems. 1980;Reidel, Dordrecht.
6. Lazer A. C., Leach D. E. Bounded perturbations of forced harmonic oscillations at resonance. Ann. Mat. Pura. Appl. 82:1969;49-68.
7. Cesar L. Nonlinear Problems Across a Point of Resonance for Non-Self-Adjoint Systems. 1978;Academic Press, San Diego. p. 43-67.
8. Schuur J. D. Perturbation at resonance for a fourth order ordinary differential equation. J. Math. Anal. Appl. 65:1978;20-25.
9. Nagle R. K., Sinkala Z. Semilinear equations at resonance where the kernel has dimension two. Differential Equations: Stability and Control. 1991;Dekker, New York.
10. Nagle R. K., Sinkala Z. Existence of 2π Nonlinear Anal. 25:1995;1-16.
11. S. W. Ma, Z. C. Wang, J. S. Yu, Coincidence degree and periodic solutions of Duffing equations, Nonlinear Anal.
12. Drabek P., Invernizzi S. Periodic solutions for systems of forced coupled pendu lum-like equations. J. Differential Equations. 70:1987;390-402.
13. Ding T. R. Nonlinear oscillations at a point of resonance. Sci. China Ser. A. 1:1982;1-13.
14. D. Y. Hao, S. W. Ma, Semilinear Duffing equations crossing resonance points, J. Differential Equations.
15. Deimling K. Nonlinear Functional Analysis. 1985;Springer-Verlag, Berlin/New York.
16. Mawhin J. Topological Degree Methods in Nonlinear Boundary Value Problems. CBMS. 40:1979;Amer. Math. Soc. Providence.
17. Mawhin J. Equivalence theorems for nonlinear operator equations and coincidence degree theory for some mappings in locally convex topological vector spaces. J. Differential Equations. 12:1972;610-636.