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June 27, 2026Boundary Value ProblemsOpen Access

Existence and multiplicity results for singular elliptic problems with logarithmic source terms and Orlicz growth

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Authors

SBSalah Boulaaras

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Overview

Randomized trial investigates weak solutions and multiplicity in nonlinear elliptic problems with logarithmic sources.

Key Points

  • The aim is to find and prove the existence of weak solutions to nonlinear elliptic boundary value problems with specific growth conditions.
  • Investigated the Dirichlet problem involving Hardy-type singular potentials and logarithmic source terms.
  • Applied Orlicz–Sobolev framework and Hardy-type inequalities to establish weak solutions.
  • Utilized a Nehari-manifold approach to demonstrate solution multiplicity for small λ values.
  • Proved the existence of nontrivial weak solutions under the defined growth conditions.
  • Established multiplicity results for solutions when λ is small using the Nehari manifold technique.
  • Demonstrated the convergence and stability of a conforming finite element discretization in the presence of singularities.

Cite This Study

Salah Boulaaras (2026) studied this question.

synapsesocial.com/papers/6a3f6972aea7db3c19540438https://doi.org/10.1186/s13661-026-02321-w
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