Non-existence of solutions for non-autonomous elliptic systems of Hamiltonian type

TL;DR

This paper generalizes Pohozaev's identity to non-autonomous elliptic Hamiltonian systems, offering a simpler method and extending previous results by Mitidieri, Van der Vorst, and Bozhkov.

Contribution

It introduces a generalized Pohozaev identity for non-autonomous elliptic systems of Hamiltonian type, simplifying existing approaches and broadening their applicability.

Findings

Provides a new, simplified proof of non-existence results.

Extends classical identities to more general systems.

Unifies previous results under a broader framework.

Abstract

We extend the classical Pohozaev's identity to semilinear elliptic systems of Hamiltonian type, providing a simpler approach, and a generalization, of the results of E. Mitidieri [6], R.C.A.M. Van der Vorst [14], and Y. Bozhkov and E. Mitidieri [1].