(11) If the solution of (10) is unique then we have the following unique solution to (11): widetilde{R}(t)=e^{nu t}R t).
However, the problem is not that there is no solution to b, but that there are "too many" solutions, i.e. there is no unique solution to b1, b2 and b3, unless some constraints are imposed on the estimation of b [ 31, 32].
As explorations have often led students to pattern formulations (e.g., see Panaoura, 2012; Suh & Moyer-Packenham, 2007), problem solving was usually constructed within defined stages, leading students toward finding numerical answers or unique solutions to the stated problems (e.g., see Chen & Liu, 2007; Hwang & Hu, 2013).
(5.2) λ has a unique solution (u_{lambda}in E) for any (lambdain R); (u_{lambda}) is increasing with respect to λ; (c_{1}d(x leq u_{lambda}(x leq c_{2}d(x)) for any (xin Omega) and some (c_{1}) and (c_{2} > 0) independent of x; (u_{lambda}in C^{1,1-mu}(Omega)).
(u(x) in L^{p}(Omega)) is the unique solution of (E) if and only if (u(x) in(A+C ^{-1}0).
For any ( a, b, x ) ∈ V 1 × V 2 × V, according to the homotopy invariance property of the Brouwer degree, we conclude that the equation Λ ( a, b, x ) = 0 has its (unique) solution on E ∗ ¯.
If the spectrum σ ( A ) of A does not intersect the imaginary axis, then for all h ∈ E 0 ( X ), there exists a unique solution in E 0 ( X ) of the differential equation u ′ ( t ) = A u ( t ) + h ( t ).
Using the theory of age-structured dynamical systems introduced in [36, 37], one can show that system (1.4) has a unique solution ((S t), e(cdot,t), i(cdot,t), T t))) satisfying the boundary conditions (1.5) and the initial condition (1.6).
Then, congruence z = x 1 e ⋅ w mod n has a unique solution because gcd (e, ϕ(n)) = 1.
