What does this research mean for the field?

A nonlinear fractional boundary value problem involving a p-Laplacian-type ψ-Hilfer operator with a logarithmic source term possesses at least three distinct weak solutions under homogeneous Dirichlet boundary conditions. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To establish the existence of multiple weak solutions for a one-dimensional nonlinear fractional boundary value problem involving a p-Laplacian-type ψ-Hilfer operator with a logarithmic source term under homogeneous Dirichlet boundary conditions.

August 27, 2026Georgian Mathematical Journal

Existence of three weak solutions for a fractional problem with logarithmic nonlinearity involving the ψ-Hilfer operator

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Authors

SBSalah Boulaaras ASAbdelaziz Sabiry

Discussion

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Overview

Theoretical analysis demonstrates the existence of at least three distinct weak solutions in fractional differential equations, extending variational models to logarithmic nonlinearities.

Key Points

To establish the existence of multiple weak solutions for a one-dimensional nonlinear fractional boundary value problem involving a p-Laplacian-type ψ-Hilfer operator with a logarithmic source term under homogeneous Dirichlet boundary conditions.
Constructed an energy functional on a reflexive Banach space within a variational framework.
Established analytical properties of the functional, verifying coercivity and the Palais–Smale condition to overcome difficulties caused by slow logarithmic growth.
Applied the Bonanno–Marano-type three critical points theorem to determine solution multiplicity.
Proved the existence of at least three distinct weak solutions for the ψ-Hilfer fractional boundary value problem.
Demonstrated that variational critical point techniques remain effective under slow-growth logarithmic nonlinearities, distinguishing this framework from conventional polynomial-growth models.

Cite This Study

Boulaaras et al. (2026) studied this question.

synapsesocial.com/papers/6a8fe9b910c91c1e926218bc https://doi.org/10.1515/gmj-2026-3037

View Full Paper

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August 27, 2026Georgian Mathematical Journal

Existence of three weak solutions for a fractional problem with logarithmic nonlinearity involving the ψ-Hilfer operator

View Full Paper

Ask AI

Bookmark

Authors

SBSalah Boulaaras ASAbdelaziz Sabiry

Discussion

Member takes

Overview

Theoretical analysis demonstrates the existence of at least three distinct weak solutions in fractional differential equations, extending variational models to logarithmic nonlinearities.

Key Points

To establish the existence of multiple weak solutions for a one-dimensional nonlinear fractional boundary value problem involving a p-Laplacian-type ψ-Hilfer operator with a logarithmic source term under homogeneous Dirichlet boundary conditions.
Constructed an energy functional on a reflexive Banach space within a variational framework.
Established analytical properties of the functional, verifying coercivity and the Palais–Smale condition to overcome difficulties caused by slow logarithmic growth.
Applied the Bonanno–Marano-type three critical points theorem to determine solution multiplicity.
Proved the existence of at least three distinct weak solutions for the ψ-Hilfer fractional boundary value problem.
Demonstrated that variational critical point techniques remain effective under slow-growth logarithmic nonlinearities, distinguishing this framework from conventional polynomial-growth models.

Cite This Study

Boulaaras et al. (2026) studied this question.

synapsesocial.com/papers/6a8fe9b910c91c1e926218bc https://doi.org/10.1515/gmj-2026-3037

View Full Paper

Ask AI

Bookmark