Results for twin singular nonlinear problems with damping term (Q539366)

Summary: The aim of this paper is to establish some new and general results on the existence of a positive solution to singular boundary value problems with damping term \[ u''(t)-\lambda u'(t)+h(t)f(t,u(t))=0,\quad a<t<b, \] \[ u'(a)-\lambda u(a)=0,\quad \gamma u (b)+\delta u'(b)=\sum^n_{i=1}a_i u(t_i), \] \[ \gamma u(a)+\delta u'(a)=\sum^n_{i=1}a_iu(t_i),\quad u'(b)-\lambda u(b)=0. \] By using the functional type cone expansion and compression fixed-point theorem in cones, some new and general results on the existence of a positive solution are obtained. An example is given to illustrate our results.