Algebraic topological techniques for elliptic problems involving fractional Laplacian

TL;DR

This paper applies algebraic topological methods to establish the existence of infinitely many bounded solutions for elliptic problems involving the fractional Laplacian, advancing the mathematical understanding of such nonlocal operators.

Contribution

It introduces a novel application of algebraic topology techniques to fractional Laplacian elliptic problems, proving the existence of infinitely many solutions.

Findings

Existence of infinitely many solutions proved.

Solutions are shown to be bounded.

Method bridges algebraic topology and fractional PDEs.

Abstract

We prove the existence of infinitely many solutions to an elliptic problem by borrowing the techniques from algebraic topology. The solution(s) thus obtained will also be proved to be bounded.