Sentence examples for infinity of solutions from inspiring English sources

Among the infinity of solutions, there is of course an optimum in terms of cost versus beam quality.

Finally, whatever the fuzzy system under consideration, there is no need to study its invertibility beforehand since the algorithm is able to handle all possible situations (no solution, one unique solution, multiple solutions, an infinity of solutions).

In this paper we establish new results concerning existence and behavior at infinity of solutions for the nonlinear quasilinear problem.

Finally in Section 5, we obtain the infinity of solutions by the Fountain Theorem and the Dual Fountain Theorem when f satisfies a special form.

where the continuous function g : R → R has a zero at x 0 and is positive everywhere else, possesses an infinity of solutions if and only if ∫ x 0 + d u g ( u ) < + ∞.

We present a set of restrictions on the fractional differential equation x ( t ) = g ( x ( t ) ), t ≥ 0, where α ∈ ( 0, 1 ) and g ( 0 ) = 0, that leads to the existence of an infinity of solutions (a continuum of solutions) starting from x ( 0 ) = 0.

We prove that any entire radial solutions of (0.1) must be one of topological, non-topological and mixed type solutions, and completely classify the asymptotic behaviors at infinity of these solutions.

Note that an infinity of smoother solutions exists [31].

It is of particular interest in the theory of qualitative analysis of differential equations to determine the exact asymptotic behavior at infinity of the solutions under the appropriate assumptions for the coefficients of an equation.

18 of the 23 models for which there is a complete equilibration are actually under-constrained and appear to have an infinity of such solutions (typically linear relations between variables).

Assumption (16) guarantees the continuability at infinity of any solution of (1) and its role is discussed in Remark 1.