#### Document Type

Article

#### Publication Date

1984

#### Abstract

We consider perturbations of the problem (*) - *x*'' + *bx* = lambda *ax*, *x*(0) - *x*(1) = 0 = *x'*(0) - *x'*(1) both by changes of the boundary conditions and by addition of nonlinear terms. We assume that at lambda = lambda 0 there are two linearly independent solutions of the unperturbed problem (*) and that *a*(dot) is bounded away from zero. When only the boundary conditions are perturbed either the Hill’s discriminant or the method of Lyapunov–Schmidt reduces the problem to 0 = det ((lambda - lambda 0)*A* - epsilon *H*) + higher order terms, where *A* and *H* are real 2 times 2 constant matrices. ...

The method of Lyapunov-Schmidt is used to analyse the full nonlinear problem. In a sequel to this paper we will analyse the bifurcation problem from a "generic" point of view and we will present some numeric examples.

#### Repository Citation

Turyn, L.
(1984). Perturbation of Periodic Boundary-Conditions. *SIAM Journal on Mathematical Analysis, 15* (4), 648-655.

https://corescholar.libraries.wright.edu/math/15

#### DOI

10.1137/0515050