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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.16 No.2

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VARIATIONAL APPROACH AND THE NUMBER OF THE NONTRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF THE SYSTEM OF THE NONTRIVIAL SUSPENSION BRIDGE EQUATIONS

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2009, v.16 no.2, pp.199-212
Jung, Tack-Sun
Choi, Q-Heung
Jung,, T. , & Choi,, Q. (2009). VARIATIONAL APPROACH AND THE NUMBER OF THE NONTRIVIAL PERIODIC SOLUTIONS FOR A CLASS OF THE SYSTEM OF THE NONTRIVIAL SUSPENSION BRIDGE EQUATIONS. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 16(2), 199-212.

Abstract

We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.

keywords
system of the nonlinear suspension bridge equations, abstract version of critical point theory on the manifold, variational linking inequality, <tex> $(P.S)^*$</tex> condition

Reference

1.

(1996). . J. Funct. Anal., , 107-136.

2.

(1985). . Nonlinear Anal., 9, 1401-1433.

3.

(2001). . J. Differential Equations, 170, 157-179.

4.

5.

(1999). . Nonlinear Analysis TMA, 35, 649-668.

6.

(2002). . Discrete and Impulsive Systems Series A: Mathematical Analysis, 9, 29-38.

7.

(1993). . Applicable Analysis, 50, 73-92.

8.

(1990). . Ann. Mat. Pura Appl., 156, 37-71.

9.

(1993). . Dynam. Report, 3, 1-23.

10.

(1996). . J. Differential Equations, 132, 222-238.

11.

(1987). . Archive for Rational Mechanics and Analysis, 98(2), 167-177.

12.

(1995). . Dynam. Systems Appl., 4, 147-156.

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics

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