Higher order non-resonance for differential equations with singularities

Mathematical Methods in the Applied Sciences

Volumn 26, Issue 12, 2003, Pages 1067-1074

  Yan, Ping ^a   Zhang, Meirong ^a  

^a TSINGHUA UNIVERSITY   (China)

Author keywords

Eigenvalue; Positive periodic solution; Repulsive singularity; Singular equation

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FUNCTIONS; PROBLEM SOLVING; THEOREM PROVING;

REPULSIVE SINGULARITY; SINGULAR EQUATION;

DIFFERENTIAL EQUATIONS;

EID: 0043175345     PISSN: 01704214     EISSN: None     Source Type: Journal    
DOI: 10.1002/mma.413     Document Type: Article

References (15)

1. Bevc V, Palmer JL, Süsskind C. On the design of the transition region of axis-symmetric magnetically focused beam valves. Journal of British Institute of Radio Engineers 1958; 18:696-708.
2. Ding T. A boundary value problem for the periodic Brillouin focusing system. Acta Scientiarum Naturalium Universitatis Pekinensis 1965l 11(1):31-38 [in Chinese].
3. Rachůnková I, Tvrdý M, Vrkoč I. Existence of nonnegative and nonpositive solutions for second order periodic boundary value problems. Journal of Differential Equations 2001; 176:445-469.
4. Torres PJ. Existence and uniqueness of elliptic periodic solutions of the Brillouin electron beam focusing system. Mathematical Methods in Applied Sciences 2000; 23:1139-1143.
5. Zhang M. Periodic solutions of Liénard equations with singular forces of repulsive type. Journal of Mathematical Analysis and Applications 1996; 203:254-269.
6. Zhang M. A relationship between the periodic and the Dirichlet BVPs of singular differential equations. Proceedings of Royal Society of Edinburgh Section A 1998; 128:1099-1114.
7. García-Ripoll JJ, Pérez-García VM, Torres P. Extended parametric resonances in nonlinear Schrödinger systems. Physical Review Letters 1999; 83:1715-1718.
8. -3 = 0. Proceedings of American Mathematical Society 1950; 1:681.
9. Ortega R. The twist coefficient of periodic solutions of a time-dependent Newton equation. Journal of Dynamics and Differential Equations 1992; 4:651-665.
10. Del Pino MA, Manásevich RF, Montero A. T-periodic solutions for some second order differential equations with singularities. Proceedings of Royal Society of Edinburgh Section A 1992; 120:231-243.
11. Magnus W, Winkler S. Hill's Equations. Dover: New York, 1979.
12. Zhang M. The rotation number approach to eigenvalues of the one-dimensional p-Laplacian with periodic potentials. Journal of London Mathematical Society 2001; 64:125-143.
13. Fonda A, Mawhin J. Quadratic forms, weighted eigenfunctions and boundary value problems for nonlinear second order ordinary differential equations. Proceedings of Royal Society of Edinburg Section A 1989; 112:145-153.
14. Mawhin J. Topological degree and boundary value problems for non-linear differential equations. In Topological Methods for Ordinary Differential Equations, Furi M, Zecca P (eds). Lecture Notes in Mathematics, vol. 1537, Springer-Verlag: New York/Berlin, 1993; 74-142.
15. Capietto A, Mawhin J, Zanolin F. Continuation theorems for periodic perturbations of autonomous systems. Transactions of American Mathematical Society 1992; 329:41-72.