# nontrivial solution

## nontrivial solution

[¦nän′triv·ē·əl sə′lü·shən]
(mathematics)
A solution of a set of homogeneous linear equations in which at least one of the variables has a value different from zero.
References in periodicals archive ?
In the literature, any eventually nontrivial solution x [member of] [M.
It's well known that every nontrivial solution of (1) is entire and of infinite order.
Due to the special structure of the nonlinear Schrodinger equation, the Jacobian operator exhibits one eigenvalue that moves to zero when the Newton iterate converges to a nontrivial solution and is exactly zero at a solution.
One nontrivial solution is constructed using the classical mountain pass theorem.
For nontrivial solution the determinant of the coefficient matrix [W([alpha], [xi], [[eta].
The vanishing determinant of a nontrivial solution to Eq.
Next, using Morse theory, we will produce a third nontrivial solution for problem (1.
For a nontrivial solution of (18), the determinant of coefficient matrix should be zero.
A complex frequency is introduced in order to find a nontrivial solution of characteristic Equations [9,10] that permits then to find the surface current (more precisely the coefficients of the basis functions expansion used to approximate the surface current).
Let the functions r(t) > 0 and u(t) exist for every nontrivial solution x(t), t [member of] [J.

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