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arXiv · 2403.03195

Concentration-compactness via profile decomposition for systems of coupled Schrödinger equations of Hamiltonian type

Anderson Cardoso·João Marcos do Ó·Diego Ferraz
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Abstract

We analyse Hamiltonian-type systems of second-order elliptic PDE invariant under a non-compact group and, consequently, involve a lack of compactness of the Sobolev embedding. We show that the loss of compactness can be compensated by using a concentration-compactness principle via weak profile decomposition for bounded Palais-Smale sequences in Banach spaces. Our analysis to prove the existence of ground states involves a reduction by the inversion method of the system to a fourth-order equation combined with a variational principle of a minimax nature. Among other results, including regularity and a Pohozaev-type identity, we also prove the non-existence of weak solutions for a class of Lane-Emden systems.

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Anderson Cardoso, João Marcos do Ó, Diego Ferraz. 2024-03-05. Concentration-compactness via profile decomposition for systems of coupled Schrödinger equations of Hamiltonian type. https://arxiv.org/abs/2403.03195

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