Asymptotically linear beam equation and reduction method
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We prove a theorem which shows the existence of at least three π-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.
Abstract
We prove a theorem which shows the existence of at least three π-periodic solutions of the wave equation with asymptotical linearity. We obtain this result by the finite dimensional reduction method which reduces the critical point results of the infinite dimensional space to those of the finite dimensional subspace. We also use the critical point theory and the variational method.
참고문헌 (4)
- V. Benci, "Critical point theorems for inde nite functionals", Invent. Math, 52, pp.241~273 (1979)
- Q.H. Choi, "An application of a variational reduction method to a nonlinear wave equation", J. Differential Equations, 117(2), pp.390~410 (1995)
- Q.H. Choi, "Multiple periodic solutions of a semilinear wave equation at double external resonances", Commun. Appl. Anal, 3(1), pp.73~84 (1999)
- P.H. Rabinowitz, "Free vibrations for a semilinear wave equation", Comm. Pure Appl. Math, 31, pp.31~68 (1968)