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This implies that is a solution of (3.8).
This proves that is a solution of (3.2).
Let, and notice that is a solution of (1.1).
It follows from (3.71) and (3.74) that is a solution of the functional equation (1.6).
Step 4. Show that is a solution of BVP (1.1), (1.2).
A function x that is a solution of (3) is called an extremal for J.
Assume that is a solution of (1.9).
Now, showing that is a solution of.
so that is a solution of (1.2).
which means that is a solution of (3.1).
We will prove that is a solution of (2.7) for.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.
Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com