Corpus ID: 203838090

# 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}
}
• Published 2019
• Mathematics
• arXiv: Analysis of PDEs
• In this paper we consider the existence and multiplicity of weak solutions for the following class of fractional elliptic problem \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. 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

## Towards a Brezis–Oswald-type result for fractional problems with Robin boundary conditions

• Mathematics
• 2020

#### References

##### Publications referenced by this paper.
SHOWING 1-10 OF 43 REFERENCES

## Fractional elliptic problem in exterior domains with nonlocal Neumann boundary condition

• Mathematics
• 2018
VIEW 1 EXCERPT

## Existence and concentration of solution for a class of fractional elliptic equation in $$\mathbb {R}^N$$RN via penalization method

• Mathematics
• 2015

## Fractional elliptic problems with critical growth in the whole of $\R^n$

• Mathematics
• 2015

## Ground state solutions for fractional scalar field equations under a general critical nonlinearity

• Mathematics
• 2016

## Existence of a Positive Solution for a Nonlinear Elliptic Equation with Saddle-like Potential and Nonlinearity with Exponential Critical Growth in $${\mathbb{R}^{2}}$$R2

VIEW 17 EXCERPTS

## Singularly perturbed Neumann problem for fractional Schrödinger equations

VIEW 1 EXCERPT

## Concentration Phenomena for Fractional Elliptic Equations Involving Exponential Critical Growth

• Mathematics
• 2015

## Uniqueness of non-linear ground states for fractional Laplacians in $${\mathbb{R}}$$R

• Mathematics
• 2013
VIEW 1 EXCERPT

## Nonlocal problems with Neumann boundary conditions

• Mathematics
• 2014
VIEW 5 EXCERPTS
HIGHLY INFLUENTIAL

## Uniqueness of Radial Solutions for the Fractional Laplacian

• Mathematics, Physics
• 2013