PERIODIC SOLUTIONS OF A QUASILINEAR WAVE EQUATIONS WITH VARIABLE COEFFICIENTS.
Abstract and keywords
Abstract (English):
We prove existence theorem for periodic in time solutions of quasilinear wave level of variable coefficients and homogeneous boundary conditions, one of which is a Neumann condition.

Keywords:
wave equation, periodic solution, sturm-liouville, fourier series.
Text
Publication text (PDF): Read Download
References

1. Barby, V. Periodic solutions to nonlinear one dimensional wave equation with x - dependent coefficients/ V. Barby, N. H. Pavel // Trans. Amer. Math. Soc.-1997.-V. 349. - № 5.- P. 2035-2048.

2. Rabinowitz, P. Free vibration for a semilinear wave equation/ P. Rabinowitz//Comm. Pure Aple. Math.-1978.- V. 31.- № 1.- P. 31-68.

3. Bahri, А. Periodic solutions of a nonlinear wave equation/A. Bahri, H. Brezis// Proc. Roy. Soc. Edinburgh Sect. A. - 1980.- V. 85. - P. 3130-320.

4. Brezis, H. Forced vibration for a nonlinear wave equations/ H. Brezis, L. Nirenberg //Comm. Pure Aple. Math.-1978. - V. 31. - № 1.- P. 1-30.

5. Plotnikov, P. I. Existence of a countable set of periodic solutions of the forced vibration problem for the weakly nonlinear wave equation / P. I. Plotnikov // Mathematical Proceeding.-1988. - Vol. 136(178).-No. 4(8). - pp. 546-560.

6. Feireisl, E. On the existence of periodic solutions of a semilinear wave equation with a superlinear forcing term/ E. Feireisl //Chechosl. Math. J.- 1988.-V. 38.- № 1.- P.- 78-87.

7. Rudakov, I.A. Nonlinear string oscillations / I.A. Rudakov // Bulletin of MSU. Ser. 1, math., mech. - 1984. - No. 2. - pp. 9-13.

8. Rudakov, I. A. Periodic solutions of the nonlinear wave equation with nonconstant coefficients/ I. A. Rudakov // Mathematical notes.-2004. - Vol. 76. - Issue 3. - pp. 427-438.

9. Shuguan, J. Time periodic solutions to a nonlinear wave equation with - dependet coefficients/ J. Shu-guan//Calc. Var. -2008.-V. 32. - P. 137-153.

10. Rudakov, I.A. Periodic solutions of a quasilinear wave equations with variable coefficients/ I. A. Rudakov // Mathematical Proceeding.-2007. - Vol. 198. - No. 4(8). - pp. 546-560.

11. Trikomi, T. Differential equations / F.Trikomi. - M.: URSS, 2003.-351 p.

12. Babich, V. M. Orthogonal decomposition and the Fourier method / V. M. Babich, N. S. Grigorieva. - L.: Publishing House of LSU, 1983. - 239 p.

13. Rudakov, I.A. Nonlinear equations satisfying a non-resonance condition / I.A. Rudakov // Proceedings of the Seminar named after I. G. Petrovsky.-2006. - Issue 25. - pp. 226-243.

14. Rudakov, I.A. Periodic solutions of the nonlinear wave equation with homogeneous boundary conditions / I.A. Rudakov // Proceedings of RAS. - 2006. - No. 1. - pp. 1-10.

Login or Create
* Forgot password?