Sentence examples for boundary value condition in from inspiring English sources

The boundary value condition in BVP (1) is more general.

This paper investigates the existence and asymptotic behavior of solutions for weighted -Laplacian integro-differential system with multipoint and integral boundary value condition in half line.

Compared with the Dirichlet boundary value condition in [14], the Neumann boundary value condition causes an additional difficulty in establishing some a priori estimates.

Theorem 3.2 Let u be the unique nonnegative bounded solution of (1.1) with the homogeneous boundary value condition in the sense of Definition  3.1.

Estimates below: Let u be a nonnegative bounded solution of (1.1) with homogeneous boundary value condition in the sense of Definition 3.1, u ≤ M. for some M > 0. For r > 0 let Ω r ≡ { x ∈ Ω | d ( x, ∂ Ω ) ≥ r }, Ω r, t ≡ Ω r × [ s, t ], ∀ s < t ≤ T, and μ ( r ) ≡ inf ( x, τ ) ∈ Ω r, t u ( x, τ ).

So, the anti-periodic boundary value conditions in (1.2) in the present paper are more suitable than those in (1.5) and (1.6).

However, to the best of our knowledge, few papers can be found in the literature for the impulsive fractional differential equations with boundary value conditions in abstract spaces.

In this section, we will transform the nonlinear second-order ordinary differential equation (1) with three-point boundary value conditions in (2 - 5) into Hammerstein integral equations.

In the following, by considering the boundary value conditions in the cases of III and IV, we give Theorems 3 and 4, respectively.

(10) Then the unknowns (varphi'(a)) and (varphi(a)) in (10) will be determined by using the boundary value conditions in (8), respectively.

This paper generally focuses on the nonlinear second-order ordinary differential equation with four cases of three-point boundary value conditions in (1 - 5).