Sentence examples similar to with two distinct solutions from inspiring English sources

The results indicate that two distinct solution branches exist beyond the onset of traveling wave flutter.

Let (u_{1}), (u_{2}) be two distinct solutions of problem (15) associated with measurable selections (f_{1,q}, f_{2,q} subset F_{q}).

Formulation of the OWF interconnection system with two different cable sizing methods (full and partial), offering two distinct solutions according to the seabed conditions or cable installation constraints.

Since eigenvalues intersect at two frequencies, smooth decomposition and spectrally majorized decomposition result two distinct solutions.

Then, problem(1.1) has at least two distinct solutions in H T 1. Theorem 1.4.

In this section, we derive some sufficient conditions under which the functional φ admits at least two distinct critical points; consequently, (1.1) admits at least two distinct solutions.

Note that four distinct solutions appear, depending on the signs of the non-constant roots.

It was of interest to examine how their sampled initial concentrations correlated with the eight distinct solutions found.

admits at least three distinct solutions.

Then (1.1) has at least three distinct solutions.

Furthermore, problem (1.2) admits at least three distinct solutions.