## Abstract

We consider the boundary value problem Lu(x) = p(x)u(x) + g(x, u^{(0)}(x),...,u^{(2m-1})(x))u(x), x?(0,p), (*) where (i) L is a 2mth order, self-adjoint, disconjugate ordinary differential operator on [0, p], together with separated boundary conditions at 0 and p; (ii) p is continuous and p = 0 on [0, p], while p ? 0 on any interval in [0, p]; (iii) g: [0, p] × R^{2m} ?R is continuous and there exist increasing functions ?_{u}, ?_{l} : [0, 8) ? [0, 8) such that with lim_{t?}_{8} ?_{l}(t) = 8 (the non-linear term in (*) is superlinear as u(x) ? 8). We obtain a global bifurcation result for a related bifurcation problem. We then use this to obtain infinitely many solutions of (*) having specified nodal properties. © 2002 Elsevier Science (USA). All rights reserved.

Original language | English |
---|---|

Pages (from-to) | 461-472 |

Number of pages | 12 |

Journal | Journal of Differential Equations |

Volume | 188 |

Issue number | 2 |

DOIs | |

Publication status | Published - 1 Mar 2003 |