## 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.

Original language | American English |
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Journal | SIAM Journal on Mathematical Analysis |

Volume | 15 |

DOIs | |

State | Published - Jan 1 1984 |

## Disciplines

- Applied Mathematics
- Applied Statistics
- Mathematics
- Physical Sciences and Mathematics
- Statistics and Probability