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arXiv · 2607.19076

Ground state solutions for Hartree type equations driven by superposition operators and Pohozaev Identity

Alessandro Cannone·Silvia Cingolani·Serena Dipierro
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Abstract

We investigate Hartree-type equations driven by a nonlocal operator $\mathcal{L}_\mu$, defined as a superposition of fractional Laplacians through a signed Borel measure $\mu$. Under Berestycki-Lions type assumptions, we prove the existence of a Mountain Pass solution and show that its energy level coincides with the minimum on the Pohozaev manifold. We also establish the boundedness of non-negative solutions. The proof of this fact requires a careful use of the Sobolev embedding in the iterative argument and a delicate treatment of the integrals involved in the estimates, as well as a Kato-type inequality in our general setting. Finally, we establish a general Pohozaev identity for solutions under a suitable summability assumption.

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Alessandro Cannone, Silvia Cingolani, Serena Dipierro. 2026-07-21. Ground state solutions for Hartree type equations driven by superposition operators and Pohozaev Identity. https://arxiv.org/abs/2607.19076

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