Sentence examples for unique solvability of this from inspiring English sources

The unique solvability of this variational inequality implies that (tilde{xi}=xi_{t^).

We established the Conti-Opial type theorems for the solvability and unique solvability of this problem.

We also apply this result to the Maxwell Schrödinger equations in the Lorentz gauge and prove unique solvability of this system in the energy space.

Φ − 1 ( u ) = | u | q − 2 u being the inverse function of Φ, and the integrability assumption on the functions r 1 − q, c, w implies the unique solvability of this system.

Observe that the unique solvability of this inequality follows from the monotonicity of A and the strict monotonicity of U s. Indeed, let x1 and x2 be two different solutions of (14).

In this paper, we consider the Cauchy problem { u ″ ( t ) = f ( t, u ( t ), u ′ ( t ) ), for almost every  t ∈ [ 0, 1 ], u ( 0 ) = 0, u ′ ( 0 ) = λ, where f is a mapping from [ 0, 1 ] × ( 0, ∞ ) × R into ℝ and λ ∈ R with λ > 0. We prove the unique solvability of this Cauchy problem using the Banach fixed point theorem.

For this, unique solvability of the Dirichlet boundary value problem in Ω 1 had to be assumed.

In this paper the unique solvability of the analog of the Tricomi problem for the third order loaded differential and integro-differential equations with parabolic-hyperbolic operators is proved.

By necessity, we have the unique solvability of the main equation (18), so the equivalent system (38 - 39 38 - 39quely solvable, and the operator ((is+ tilde{R}(x))) has a bouniquelyversolvable

In this section, we research the unique solvability of the difference scheme (9) by use of the Fourier analysis method.

This paper only focuses on the unique solvability of the CCD system for solving the convection-diffusion equation.