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Step 3. A lower solution of.
Obviously, is a lower solution of (1.1).
Finally, let α be a lower solution for (3.1).
Obviously, is a lower solution of (1.1)–(1.3) in.
We now construct a lower solution of (3.13).
By Proposition 2.3, problem (2.11) has a lower solution.
On the other hand, is a weak lower solution.
Step 4 ( is a weak lower solution of (1.1)).
We will use the upper and lower solution method.
Obviously, (check{u}=0) is a lower solution of (2.4).
whence it follows that is a weak lower solution to.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com