The phrase "a unique solution of the form" is correct and usable in written English.
It can be used in mathematical or technical contexts when describing a specific type of solution to a problem or equation.
Example: "The analysis reveals that there is a unique solution of the form f(x) = ax^2 + bx + c."
Alternatives: "a distinct solution of the type" or "a singular solution in the format".
Then the system (21) has a unique solution of the form y(t)=c+^{mathrm{CF}}_{a}I^{alpha} f bigl t,y(t bigr).
are fulfilled, then the problem (8) has a unique solution of the form (9) in classes (H_{p (cdot),rho}^ times_{-1} H_{p (cdot ),rho}^ ).
The optimization problem above has a unique solution of the form, ∀ s ∈ S, x s = b s 1 β k − μ N 0 p max Ω s +, (25).
Then the system (21) has a unique solution of the form y(t)=c+^{AB}_{a}I^{alpha} f bigl t,y(t bigr).
Clearly, the Cauchy problem (22) involving the homogeneous equation _{a}^{C}nabla_{ q,h)}^{alpha}y(t -lambda y(t -lambda tinwidetilde {mathbb{T}}^{sigma^{n+1} (a)}_{(q,h)}, n-1< alphale n (26) has a unique solution of the form y(t)=0um_{k=0}^{n-1} b_{k} E^{a,quadda}_{alpha, k+1}(tinwidetilde
Then the system (24) has a unique solution of the form begin{aligned} y(t) =& c+^{AB}_{a}mathbf{I}^{alpha} fbigl t,y(t bigr) =& c+frac{2-alpha}{B alpha-1)} int_{a}^{t} fB alpha-1s)bigr),ds+ frac{alpha -1}{B(alpha-1)}bint_{a{a}I^{tlpha}fbigl sdot,y(cdot) bigr)bigr) (t).
Obviously, is a unique solution of the problem (3.1).
De Sitter's solution showed that Einstein's solution is not a unique solution of his field equations.
has a unique solution which is of the form u ( t ) = ∫ 0 ω G 1 ( t, s ) ( − h ( s ) ) d s, (3.2).
Thus given a finite-Einstein-energy solution of the equation □ƒ + λƒ3 = 0 on M0 (λ ⩾ 0) there exist unique solutions ƒ± of the free wave equation which approach ƒ in the Minkowski energy norm as x0 → ± ∞, and every finite-Einstein-energy solution of the free wave equation is of the form ƒ+ (or ƒ−) for a unique solution ƒ of the nonlinear equation.
