Sentence examples for many weak solutions from inspiring English sources

Then (1.1) possesses infinitely many weak solutions.

Then problem (1.1) admits infinitely many weak solutions.

Then problem (1.7) has infinitely many weak solutions.

Hence, problem (3.25) has infinitely many weak solutions.

Moreover, the existence of infinitely many weak solutions is obtained via the fountain theorem.

Hence, the problem (1.1) possesses infinitely many weak solutions, and the corresponding critical values are positive.

Then the system (1.1) has infinitely many nontrivial weak solutions.

Thus (GS) has infinitely many nontrivial weak solutions in E. The proof is finished.

Since r is arbitrary and ({lambda_{r}} rightarrow infty), (r rightarrowinfty), then problem (1.1) has infinitely many nontrivial weak solutions.

In the case of periodic boundary conditions and for arbitrary dimension (dgeq2), there exist infinitely many global weak solutions for the incompressible Euler equation with initial data [1].

Moreover, if F is even in z, then (GS) has infinitely many nontrivial weak solutions in E. Theorem 1.3 Let F satisfy ( F 0 ), ( F ∞ ) and ( F ∞ 2 ± ).