# The mixed BVP for second order nonlinear ordinary differential equation at resonance

Mukhigulashvili, Sulkhan (2016) The mixed BVP for second order nonlinear ordinary differential equation at resonance. Mathematische Nachrichten.

Efficient sufficient conditions are established for the solvability of the mixed problem $$u''(t)=p(t)u(t)+ f(t,u(t))+h(t), \qquad \;\;\;\; u(a)=0,\quad u'(b)=0,$$ where $h,p\in L([a,b];R)~ \text{and}~ f\in K([a,b]\times R;R),$ in the case where the homogeneous linear problem $w''(t)=p(t)w(t), \;\; w(a)=0,\;\; w'(b)=0$ has nontrivial solutions.