On the existence of solutions for singular boundary value problem of third-order differential equations

Mathematica Slovaca

Feng Wang¹  Yujun Cui¹ 

关键词: singular;    nontrivial solutions;    positive solutions;    topology degree;   

DOI  :  10.2478/s12175-010-0027-5

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

The singular boundary value problems of third-order differential equations $$egin{array}{*{20}c} { - u'''(t) = h(t)f(t,u(t)), t in (0,1),} \ {u(0) = u'(0) = 0, u'(1) = alpha u'(eta )} \ end{array} $$ are considered under some conditions concerning the first eigenvalues corresponding to the relevant linear operators, where h(t) is allowed to be singular at both t = 0 and t = 1, and f is not necessary to be nonnegative. The existence results of nontrivial solutions and positive solutions are given by means of the topological degree theory.

【 授权许可】

Unknown