TY - JOUR
AU - Mukhigulashvili, Sulkhan
AU - NovotnÃ¡, Veronika
PY - 2019/10/20
Y2 - 2022/01/27
TI - Some two-point problems for second order integro-differential equations with argument deviations
JF - Topological Methods in Nonlinear Analysis
JA - TMNA
VL - 54
IS - 2
SE -
DO -
UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2019.045
SP - 459 - 476
AB - In the paper we describe the classes of unique solvability of the Dirichlet and mixed two point boundary value problems for the second order linear integro-differential equation $$ u''(t)=p_0(t)u(t)+p_1(t)u(\tau_1(t))+\int_{a}^{b}p(t,s)u(\tau(s))ds+ q(t). $$% On the basis of the obtained and, in some sense, optimal results for the linear problems, by the a priori boundedness principle we prove the theorems of solvability and unique solvability for the second order nonlinear functional differential equations under the mentioned boundary conditions.
ER -