ORA-04031: unable to allocate X bytes of shared memory

Your application is probably not using bind variables, which has caused the SGA to become fragmented (it fills up with multiple copies of SQL that use literals instead of binds).

You can temporarily fix the problem by flushing the shared pool with:

alter system flush shared_pool;

There's a workaround you can try to stop it happening in the future.

Turn on cursor sharing, then bounce the database:

ALTER SYSTEM SET cursor_sharing='SIMILAR' SCOPE=BOTH;

The only real way of fixing this is to rewrite your application so that it uses bind variables.

If you start your instance using a server parameter file (a binary version of initialization parameter file, spfile), you can extract the initialization parameters to plain-text initialization parameter file (pfile), alter them, and then start your instance with modified memory parameters.

sql> create pfile='myinit.ora' from spfile='spfileORCL.ora';

Modify your memory-related parameters in myinit.ora and start your instance using this new configuration:

sql> startup pfile='myinit.ora';

You can then save your settings back to an spfile with the following command:

sql> create spfile='spfileORCL.ora' from pfile='myinit.ora';

And start your database as usual:

sql> startup;