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September 10, 2025MathematicsOpen Access

Three Solutions for a Double-Phase Variable-Exponent Kirchhoff Problem

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At least three solutions exist for the double-phase variable-exponent Kirchhoff problem, showcasing its complexity.
The model generalizes the Kirchhoff equation, integrating anisotropic and heterogeneous diffusion phenomena.
Regularity results are obtained for the energy functional, enabling the application of critical point theories.
An innovative n-dimensional vector inequality is introduced, enhancing understanding of the energy functional's properties.

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Analysis reveals three solutions for double-phase variable-exponent Kirchhoff problems, suggesting a novel approach to elliptic equations.

Mustafa Avcı (2025) studied this question.

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Analysis reveals three solutions for double-phase variable-exponent Kirchhoff problems, suggesting a novel approach to elliptic equations.