Sentence examples for boundary value problem possesses from inspiring English sources

It is also shown that under certain conditions there exists an interval of the control parameter in which the boundary value problem possesses infinitely many solutions.

It is proved that the corresponding initial boundary value problem possesses a unique global classical solution for any (mu>0) and (tau ge1), which is uniformly bounded in (Omegatimes 0,+infty)).

Moreover, when (g v =v) and (chi (v =mathrm{const.}:=chi>0), Tao [21] proved that if (|v_{0}|_{L^{infty}(Omega)}) is sufficiently small, then the corresponding initial boundary value problem possesses a unique global solution that is uniformly bounded.

When (D u ge c_{D} (u+1)^{m-1}) with (m>2-frac{2}{N}), Wang et al. [24] showed that the corresponding initial boundary value problem possesses a unique global classical solution that is uniformly bounded provided that (Omegasubsetmathbb{R}^{N}) is a bounded convex domain and some other technical conditions are fulfilled.

It is proved that the corresponding initial-boundary value problem possesses a global generalized solution for any sufficiently regular initial data ((n_{0}, c_{0}, u_{0})) satisfying (n_{0}geq0) and (c_{0}>0).

The initial boundary value problem (1.1)–(1.3) possesses the following conservative quantities: (14).

To be more precise, we prove that the boundary value problem (1) possesses only a trivial solution if f obeys the following slope condition: α ′ ( x ) > 2 n n − 2 α ( x ) x, where α is the anti-derivative of f with α ( 0 ) = 0 and n > 2 (see Section 4 for details).

Since the initial boundary value problem (4) possesses the property of uniqueness of its solutions, then the solution v h ( x, t ) of its homogeneous part can be written as follows: v h ( x, t ) = T ( t ) v ( x, 0 ) = T ( t ) ( g ( x ) − ψ 0 ( 1 − x ) − ψ 1 x ).

Then there exists a pair ∈ Ω 2 such that the function u : = u ∞ is a solution of the periodic boundary value problem (1), (2) possessing properties (47).

Then boundary value problem (1.1) with (1.2) possesses at least one solution.

The boundary value problem (1) and (2) is said to be consistent if it possesses at least one solution.