Abstract
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.
Citation
Sulkhan Mukhigulashvili. Veronika Novotná. "Some two-point problems for second order integro-differential equations with argument deviations." Topol. Methods Nonlinear Anal. 54 (2A) 459 - 476, 2019. https://doi.org/10.12775/TMNA.2019.045