Analysis and Numerical Solutions of Positive and Dead Core Solutions of Singular Sturm-Liouville Problems

作者：Pulverer Gernot; Stanek Svatoslav^*; Weinmueller Ewa B

来源：Advances in Difference Equations, 2010, 969536.

DOI：10.1155/2010/969536

In this paper, we investigate the singular Sturm-Liouville problem u '' = lambda g (u), u'(0) = 0, beta u'(1) + alpha u(1) = A, where lambda is a nonnegative parameter, beta >= 0, alpha > 0, and A > 0. We discuss the existence of multiple positive solutions and show that for certain values of lambda,there also exist solutions that vanish on a subinterval [0, rho] subset of [0, 1), the so-called dead core solutions. The theoretical findings are illustrated by computational experiments for g(u) = 1/root u and for some model problems from the class of singular differential equations (phi(u'))' + f (t,u') = lambda g(t, u, u') discussed in Agarwal et al. (2007). For the numerical simulation, the collocation method implemented in our MATLAB code bvpsuite has been applied.

• 出版日期2010