$L=\{ww^Rv\mid v,w\in \{a,b\}^+\}$ Is $L$ regular ?
Edit
Is it ok?
Let $p$ will be length of pumping lemma. Then, $a^pb(a^pb)^Rv\in L$.
When $a^p(a^pb)^Rv = xyz$
$p\ge |y|\ge 1 $
So $a^{p+k}b(a^pb)^Rv$. Because of the fact that $a^{p+k}b(a^pb)^R$ is not palindrom then $a^{p+k}b(a^pb)^Rv\notin L$. Thanks to pumping lemma we have $L$ is irregular.
Ok ?