Radial Solutions for Hamiltonian Elliptic Systems with Weights

TL;DR

This paper establishes the existence of infinitely many radial solutions for weighted Hamiltonian elliptic systems in Rn, introducing a new weighted embedding theorem for fractional Sobolev spaces that may have broader applications.

Contribution

It proves the existence of infinitely many solutions for weighted elliptic systems and develops a novel weighted embedding theorem for fractional Sobolev spaces.

Findings

Existence of infinitely many radial solutions for weighted elliptic systems.

Development of a weighted embedding theorem for fractional Sobolev spaces.

Potential broader applications of the embedding theorem.

Abstract

We prove the existence of infinitely many radial solutions for elliptic systems in Rn with power weights. A key tool for the proof will be a weighted imbedding theorem for fractional-order Sobolev spaces, that could be of independent interest.