# Semilinear fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions

## TL;DR

This paper investigates a nonlinear fractional elliptic boundary value problem with mixed boundary conditions, analyzing the existence and properties of solutions involving concave-convex nonlinearities.

## Contribution

It introduces new results on the existence and behavior of solutions for fractional elliptic problems with mixed Dirichlet-Neumann boundary conditions.

## Key findings

- Existence of solutions under certain conditions
- Characterization of solution behavior
- Impact of boundary conditions on solutions

## Abstract

We study a nonlinear elliptic boundary value problem defined on a smooth bounded domain involving the fractional Laplace operator, a concave-convex powers term together with mixed Dirichlet-Neumann boundary conditions.