Sentence examples for trivial solution to from inspiring English sources

However, if λ > μ + α, the stability switches from the trivial solution to the bifurcated attractor.

(8) It is obvious that (Theta(t) = 0) is a trivial solution to Eq. (8).

We prove that the system bifurcates from the trivial solution to an attractor as parameter crosses certain critical value.

In addition to a sort-based trivial solution to find optimal replacement plan, we propose a segment tree-based buffer structure to efficiently maintain optimal replacement plans.

Remark 1 The result of Theorem 6 shows that the trivial solution to Eq. (20) is uniformly stable on the initial value.

As a result, we show the system bifurcates from the trivial solution to an attractor ∑ λ as system parameter λ crosses the critical value a, the first eigenvalue of the eigenvalue problem of the linearized equation of (1.1).

The infimum over monogenic functions is natural since they are trivial solutions to an A-Dirac equation just as constants are solutions to an A-harmonic equation.

Then u is degenerate, that is, there exists a non-trivial solution to left { textstylebegin{array}{l} L_{u} v=-Delta_{mathbf{g}} v - p u^{p-1}v =0quad textit{on } A, v = 0 quad textit{on } partial A, end{array}displaystyle right.

In the domain G = { ( x ; t ) : − ∞ < t < 0, 0 < x < − t } we consider the following problem: it is required to find a non-trivial solution to the heat conduction equation − u t ∗ ( x, t ) = a 2 u x x ∗ ( x, t ), (21).

As an application, we prove the existence of non-trivial solutions to non-homogeneous q(x -Laplace equations.

In the next section, we look for a family ( y T ) T > 0, with y T ∈ C ( [ 0, 1 ], R ), of (non-trivial) solutions to (4).