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SOLVABILITY FOR A CLASS OF THE SYSTEM OF THE NONLINEAR SUSPENSION BRIDGE EQUATIONS
정택선,최규흥 호남수학회 2009 호남수학학술지 Vol.31 No.1
We show the existence of the nontrivial periodic so- lution for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition by critical point theory and linking arguments. We investigate the geometry of the sublevel sets of the corresponding functional of the system, the topology of the sublevel sets and linking construction between two sublevel sets. Since the functional is strongly indef- inite, we use the linking theorem for the strongly inde¯nite func- tional and the notion of the suitable version of the Palais-Smale condition.