The effect of boundary geometry in nonlocal critical problems with Hardy-Littlewood-Sobolev exponent

TL;DR

This paper studies how the shape of the boundary affects the existence of ground state solutions in a nonlocal boundary value problem involving Hardy-Littlewood-Sobolev critical exponents and Choquard nonlinearity.

Contribution

It analyzes the influence of boundary geometry on solution existence for a mixed Dirichlet-Neumann problem with critical nonlocal nonlinearities.

Findings

Boundary geometry significantly impacts solution existence.

Existence results depend on boundary shape and boundary conditions.

Provides new insights into nonlocal critical problems with mixed boundary conditions.

Abstract

In this paper we consider a mixed Dirichlet-Neumann boundary value problem. lem involving Choquard nonlinearity with upper critical exponent in the sense of Hardy- Littlewood Sobolev inequality. We investigate the effect of the geometry of the boundary part where the Neumann condition is prescribed on the existence problem of ground state solutions.