Some two-point problems for second order integro-differential equations with argument deviations

Sulkhan Mukhigulashvili, Veronika Novotná

DOI: http://dx.doi.org/10.12775/TMNA.2019.045

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.

Keywords


Integro-differential equations; Dirichlet and mixed problems; unique solvability; a priori boundedness principle

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