Sentence examples for boundary value problems i from inspiring English sources

If the boundary data are of Hölder class, we consider the Riemann-Hilbert boundary value problems I, II, III with variable coefficients for monogenic functions of axial type in (mathbb{R}^{4}) and null-solutions to ((mathcal{D}-alpha )phi=0), (alphainmathbb{R}).

The previous boundedness condition is anyway weaker than the one that is often used in literature in relation with boundary value problems, i.e., the following one.

In this section, we will discuss the existence of solutions of variable exponent mean curvature impulsive system periodic-like boundary value problems, i.e. the existence of solutions of (1 -(4).

In this section, we will discuss the existence of solutions of variable exponent mean curvature impulsive system Dirichlet boundary value problems, i.e. the existence of a solution of (1 - 3) and (5).

In this section, we will discuss the existence of solutions of variable exponent mean curvature impulsive system Neumann boundary value problems, i.e. the existence of a solution of (1 - 3) and (6).

Motivated by the above papers, in this article, we study a new class of fractional boundary value problems, i.e., the following fractional differential inclusions with three-point fractional integral boundary conditions: { D α c x ( t ) ∈ F ( t, x ( t ), c D β x ( t ) ), t ∈ [ 0, 1 ], 1 < α ≤ 2, 0 < β < 1, x ( 0 ) = 0, a I γ x + b x ( 1 ) = c, 0 < η < 1, (1).

Fourier series are used to solve boundary value problems in partial differential equations.

The existing discrete geodesic algorithms are mainly designed to solve the boundary value problem, i.e., to find the shortest path between two given points.

Under (4.48), the localization problem (4.39) is equivalent to the following boundary value problem, i.e. the so-called ({S}_{k}) problem.

In the case that we have a two-point boundary value problem, i.e., when the boundary conditions are fixed on the extremes of the interval, we have a two-sided Green's function, also called Green's function, only.

The BHCP is the time-inverse boundary value problem, i.e., given the information at a specific point of time, say (t=T), the goal is to recover the corresponding structure at an earlier time (t< T).