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Trudinger-Moser type inequality and existence of solution for perturbed non-local elliptic operators with exponential nonlinearity

  • Author Bio: E-mail address: bahrounianouar@yahoo.fr
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  • In this paper we consider the following perturbed nonlocal problem with exponential nonlinearity

    $\begin{cases}-\mathcal{L}_{K}u+ \left|u\right|^{p-2}u+h(u)= f \ \ \ \ \ \mbox{in} \ \ \Omega,\\u=0, \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \mbox{in}\ \ \mathbb{R}^{N}\setminus \Omega,\end{cases}$

    where $s\in (0, 1)$, $N=ps$, $p\geq 2$ and $f\in L.{\infty}(\mathbb{R}^{N})$. First, we generalize a suitable Trudinger-Moser inequality to a fractional functional space. Then, using the Ekeland's variational principle, we prove the existence of a solution of problem (1).

    Mathematics Subject Classification: Primary: 35J60; 35J91; Secondary: 58E30.


    \begin{equation} \\ \end{equation}
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