This is that besides the solution that seems to describe the symmetries of the universe, there appears to be an indefinite number of other solutions, each with its own, private set of symmetries, that do not.That need not be a problem.
However, besides the solution property, the polymer material performance also has an important influence on the formation of helical fibers.
For the sake of completeness, besides the solution above, we will provide another elementary solution in regard to the inequalities (3.7).
In particular, besides the solution, obtained using the so-called regularization approach, a simple statistical estimate of the reconstructed loads and a global measure of the accuracy are investigated.
Then, besides the solution u constructed in Theorem 3.1, problem (1.1) has another positive solution v ˜ ∈ C [ 0, 1 ] with r < ∥ v ˜ + M ω ∥ ≤ R. To show (1.1) has a positive solution, we will show (3.14) has a solution u ˜ ∈ C [ 0, 1 ] with u ˜ ( x ) > M ω ( x ) for x ∈ [ 0, 1 ] and r ≤ ∥ u ˜ ∥ ≤ R. Let X = C [ 0, 1 ] and K be a cone in X defined by (2.5).
Naturally, people want to ask whether the system owns the other solutions besides the trivial solution.
Naturally, people want to know whether there are other solutions besides the trivial solution.
According to Lemma 2.4.9 in [26], we will show that system (3) has at least one positive solution besides the bifurcation solution ((u(s),v s))) when (k_{1}) is small enough and (k_{2}) is sufficiently large with (q>frac{1}{2}).
This method, as will be seen, besides anticipating of multiplicity of the solutions of the nonlinear differential equations, calculates effectively the all branches of the solutions (on the condition that, there exist such solutions for the problem) analytically at the same time.
