Sentence examples for for equation from inspiring English sources

(for Equation 2).

We provide the proof for Equation (12).

The proof for Equation 11 is similar.

Important geometry for equation derivation is also illustrated.

We will present two different proofs for equation (5.1).

(1.4) The methods in [1] for equation (1.2), in [17] for equation (1.3) and in [18] for equation (1.4) were all based on topological degree theory, and the upper and lower solutions techniques was used in [1] for equation (1.1).

Furthermore, explicit solutions for equation (1.1) are also obtained.

Moreover, we have the following conjecture for Equation (15).

where G is the principal Green function for Equation (3.1).

Now, we give an existence theorem for equation (1.7).

For equation (1.1), one may face many difficulties.