# Multiplicity of solutions for a class of fractional elliptic problem with critical exponential growth and nonlocal Neumann condition.

@article{Alves2019MultiplicityOS, title={Multiplicity of solutions for a class of fractional elliptic problem with critical exponential growth and nonlocal Neumann condition.}, author={C. Alves and C. Ledesma}, journal={arXiv: Analysis of PDEs}, year={2019} }

In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \begin{equation}\label{00} \left\{\begin{aligned} (-\Delta)^{\frac{1}{2}}u + u &= Q(x)f(u)\;\;\mbox{in}\;\;\R \setminus (a,b)\\ \mathcal{N}_{1/2}u(x) &= 0\;\;\mbox{in}\;\;(a,b), \end{aligned} \right. \end{equation} where $a,b\in \R$ with $a<b$, $(-\Delta)^{\frac{1}{2}}$ denotes the fractional Laplacian operator and $\mathcal{N}_s$ is the nonlocal operator that… CONTINUE READING

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## Nonlocal problems with Neumann boundary conditions

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