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Problem with integral condition for evolution equation

Kalenyuk P. I., Kuduk G., Kohut I. V., Nytrebych Z. M.

Journal of Mathematics and Applications

2015

Vol. 38

71--76

We propose a method of solving the problem with non-homogeneous integral condition for homogeneous evolution equation with abstract operator in a linear space H. For right-hand side of the integral condition which belongs to the special subspace H ⊆ L, in which the vectors are represented using Stieltjes integrals over a certain measure, the solution of the problem is represented in the form of Stieltjes integral over the same measure.

Boundary Value Problems for Differential Equations with Fractional Order and Nonlinear Integral Conditions

Benchohra M., Hamani S.

Commentationes Mathematicae

2009

Vol. 49, [Z] 2

147-159

In this paper, we shall establish sufficient conditions for the existence of solutions for a class of boundary value problem for fractional differential equations involving the Caputo fractional derivative and nonlinear integral conditions.

A mixed problem for a parabolic equation of higher order with integral conditions

Mesloub S., Mezhoudi R., Medjeden M.

Bulletin of the Polish Academy of Sciences. Mathematics

2002

Vol. 50, no 3

313-322

In this paper, we investigate the solvability of a mixed problem with integral conditions for a parabolic equation of higher order. The existence and uniqueness of the strong solution are established with the help of a priori bound and the density of the image of the operator generated by the problem in consideration.