MMN-1889
The mixed BVP for the second order nonlinear ordinary differential equation at resonance
Sulkhan Mukhigulashvili;Abstract
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.
Vol. 18 (2017), No. 2, pp. 975-992