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June 27, 2026Boundary Value Problems0 citationsOpen Access

Existence and Multiplicity of Solutions for Nonlinear Elliptic Problems

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.
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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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Also Consider

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  1. 1An Orlicz space approach to exponential elliptic problems in higher dimensions2026 · 1 citations
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  4. 4Existence of three weak solutions for a fractional problem with logarithmic nonlinearity involving the ψ-Hilfer operator2026
  5. 5Regularity results to a class of elliptic equations with explicit $u$-dependence and Orlicz growth2024