High energy solution of the Choquard equation
Daomin Cao, Hang Li
TL;DR
This paper proves the existence of positive high energy solutions for the Choquard equation using global compactness analysis, especially when ground states are unattainable under certain conditions.
Contribution
It introduces a novel approach to establish high energy solutions for the Choquard equation where ground states do not exist.
Findings
Existence of positive high energy solutions proven
Ground states cannot be achieved under certain assumptions
Global compactness analysis is effective for this problem
Abstract
The present paper is concerned with the existence of positive high energy solution of the Choquard equation. Under certain assumptions, the ground state of Choquard equation can not be achieved. However, by global compactness analysis, we prove that there exists a positive high energy solution.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Nonlinear Partial Differential Equations · Stability and Controllability of Differential Equations