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This research focuses on solving a singular double-phase Kirchhoff problem involving a nonlocal integrodifferential operator.

December 11, 2025MathematicsOpen Access

Singular Double Phase Kirchhoff Type Problem with a General Nonlocal Integrodifferential Operator

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This research focuses on solving a singular double-phase Kirchhoff problem involving a nonlocal integrodifferential operator.
Reformulate the problem into an integral equation.
Derive the corresponding energy functional from this integral equation.
Combine variational methods with monotonicity techniques for analysis.
Utilize the implicit function theorem to establish weak solutions.
Demonstrated that the functional has a minimum point in an appropriate Sobolev space.
Confirmed that the minimum corresponds to a weak solution despite the singular term.

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The study uses a variational method to find weak solutions for a singular Kirchhoff problem with nonlocal operators.

Ramzi Alsaedi (2025) studied this question.

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