Sentence examples for method and compactness from inspiring English sources

Step 4: Energy method and compactness results.

In order to prove the existence of solutions, we employ the Galerkin method and compactness arguments.

Moreover, to prove the existence of a weak solution to the problem, we use the Galerkin method and compactness arguments.

In this section, we use the regularization method and compactness theorems to prove the local existence of the solutions to problem (1.1 - 1.3 1.1 - 1.3

By means of the Galerkin method and compactness criteria and a difference inequality introduced by Nakao [13], Ye [14, 15] has proved the existence and decay estimate of global solutions for the problem (1.1)–(1.3) with inhomogeneous term and.

By mean of the Galerkin method and compactness criteria and a difference inequality introduced by Nakao [18], the author [19, 20] has proved the existence and decay estimate of global solutions for the problem (1.1)–(1.3) with inhomogeneous term and.

The proof follows from the Galerkin method; and the compactness method, the procedure is very similar to the proof of Theorem 3.3, and it is even easier.

Based on the Galerkin method and the compactness theorem, we establish the existence of the global generalized solution.

We are going to prove the existence and uniqueness for problems (1.1)–(1.3) by the Galerkin method and the compactness theorem in this section.

By using the Nehari manifold method and the concentration compactness principle (see [12]) in the Orlicz space, Guo and Tang [13] considered the following equation: (1.3).

Under suitable hypotheses, we obtain the existence of a least energy solution u λ of ( E λ ) which localizes near the potential well int a − 1 ( 0 ) for λ large enough by using the variational method and the concentration compactness method in an Orlicz space.