Global bifurcation from intervals for Sturm-Liouville problems which are not linearizable

作者：Dai Guowei^*

来源：Electronic Journal of Qualitative Theory of Differential Equations, 2013, (65).

• interval bifurcation
• Sturm-Liouville problem
• unilateral global bi-furcation

In this paper, we study unilateral global bifurcation which bifurcates from the trivial solutions axis or from infinity for nonlinear Sturm{Liouville problems of the form
{-(pu')' + qu = lambda au + af (x; u; u'; lambda) + g (x; u; u'; lambda) for x is an element of (0; 1);
b(0)u(0) + c(0)u'(0) = 0;
b(1)u(1) + c1u'(1) = 0;
where a is an element of C([0; 1]; [0;+infinity)) and a(x) not equal 0 on any subinterval of [0; 1], f; g is an element of C([0; 1] x R-3;R). Suppose that f and g satisfy.
vertical bar f(x; xi; eta; lambda)vertical bar <= M-0 vertical bar xi vertical bar +M-1 vertical bar eta vertical bar; for all x is an element of [0; 1] and lambda is an element of R,
g(x; xi; eta; lambda) = o(vertical bar xi vertical bar + vertical bar eta vertical bar); uniformly in x is an element of [0; 1] and lambda is an element of Lambda,
as either vertical bar xi vertical bar + vertical bar eta vertical bar -> 0 or vertical bar xi vertical bar + vertical bar eta vertical bar -> +infinity, for some constants M-0, M-1, and any bounded interval Lambda.

• 出版日期2013
• 单位西北师范大学