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This research investigates the existence and multiplicity of weak solutions for Kirchhoff-type double-phase problems.

Critical Kirchhoff (p,q)-Equations with Lack of Compactness

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This research investigates the existence and multiplicity of weak solutions for Kirchhoff-type double-phase problems.
Utilizes variational methods to analyze critical and subcritical terms.
Examines problems with single and double parameters.
Addresses compactness issues in degenerate cases.
Proves the existence of infinitely many weak solutions with negative energy.
Demonstrates at least one positive energy solution for certain parameter conditions.
Covers variational complexities tied to critical and subcritical reaction terms.

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This work demonstrates multiple weak solutions with negative energy in Kirchhoff equations, indicating complex interactions in double-phase contexts.

Youpei Zhang (2026) studied this question.

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This work demonstrates multiple weak solutions with negative energy in Kirchhoff equations, indicating complex interactions in double-phase contexts.