Global structure of positive solutions for superlinear second-order periodic boundary value problems

作者：Ma Ruyun^*; Xu Jia; Han Xiaoling

来源：Applied Mathematics and Computation, 2012, 218(10): 5982-5988.

DOI：10.1016/j.amc.2011.11.079

• Multiplicity results
• Eigenvalues
• Bifurcation methods
• Positive solutions

We consider periodic boundary value problems of nonlinear second order ordinary differential equations of the form.
u '' - rho(2)u + lambda a(t)f(u) = 0, 0 < t < 2 pi,
u(0) = u(2 pi), u'(0) = u'(2 pi),
where rho > 0 is a constant, a is an element of C([0,1], [0,infinity)) with a(t(0)) > 0 for some t(0) is an element of [0,2 pi], f subset of C([0,infinity),[0,infinity)) and f(s) > 0 for s > 0, and f(0) = infinity, where f(0) = lim(s -> 0+)f(s)/s. We investigate the global structure of positive solutions by using the Rabinowitz's global bifurcation theorem.

• 出版日期2012-1-15
• 单位西北师范大学