On solvability of some nonlocal boundary value problems for biharmonic equation

Solvability of Nonlocal Fractional Boundary Value Problems

On solvability of some boundary value problems for a fractional analogue of the Helmholtz equation

In this paper we study some boundary value problems for fractional analogue of Helmholtz equation in a rectangular and in a half-band. Theorems about existence and uniqueness of a solution of the considered problems are proved by spectral method.

Solvability for some boundary value problems with φ-Laplacian operators

We study the existence of solution for the one-dimensional φ-laplacian equation (φ(u′))′ = λf(t, u, u′) with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate λ0 is given such that the problem possesses a solution for any |λ| < λ0.

Nonlocal Boundary Value Problems

The theory of the nonlocal linear boundary value problems is still on the level of examples. Any attempt to encompass them by a unified scheme sticks upon the lack of general methods. Here we are to outline an algebraic approach to linear nonlocal boundary value problems. It is based on the notion of convolution of linear operator and on operational calculus on it. Our operators are right inver...

On Some Boundary Value Problems for an Ultrahyperbolic Equation

The correct formulation of a characteristic problem and a Darboux type problem in the special weighted functional spaces for an ultrahyperbolic equation is investigated. In the space of variables x1, x2, y1 and y2 we consider the ultrahyperbolic equation uy1y1 + uy2y2 − ux1x1 − ux2x2 = F. (1) Denote by D : −y1 < x1 < y1, 0 < y1 < +∞, a dihedral angle bounded by the characteristic surfaces S1 : ...