Refine
Year of publication
Document Type
- Article (40)
- Preprint (35)
- Monograph/Edited Volume (27)
- Review (1)
Language
- English (103) (remove)
Is part of the Bibliography
- yes (103) (remove)
Keywords
- Fredholm property (5)
- index (5)
- Cauchy problem (4)
- Navier-Stokes equations (4)
- Toeplitz operators (4)
- Dirac operator (3)
- Quasilinear equations (3)
- Riemann-Hilbert problem (3)
- classical solution (3)
- star product (3)
We define weak boundary values of solutions to those nonlinear differential equations which appear as Euler-Lagrange equations of variational problems. As a result we initiate the theory of Lagrangian boundary value problems in spaces of appropriate smoothness. We also analyse if the concept of mapping degree of current importance applies to the study of Lagrangian problems.
We consider a solution of the nonlinear Klein-Gordon equation perturbed by a parametric driver. The frequency of parametric perturbation varies slowly and passes through a resonant value, which leads to a solution change. We obtain a new connection formula for the asymptotic solution before and after the resonance.