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<p>We study a Kirchhoff-type elliptic equation with variable exponent growth, logarithmic nonlinearities and nonlocal terms. The analysis is based on two complementary operator decompositions. For the existence result, the equation is written as the sum of a principal Kirchhoff diffusion operator and a perturbation; the main part is treated via the Minty–Browder theorem while the remaining terms are handled through a Mawhin-type continuation degree argument. A second decomposition is then introduced to establish uniqueness by isolating a monotone component of the operator. This approach yields existence and uniqueness of weak solutions under assumptions weaker than those usually required in variational settings.</p>

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A Minty–Browder–Mawhin approach to Kirchhoff problems with variable exponents

  • 期刊论文

  • 发表日期：

    2026年8月1日

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  • El-mahdi Nafia,
  • Abdelmjid Benmerrous,
  • M’ Hamed El Omari

摘要

We study a Kirchhoff-type elliptic equation with variable exponent growth, logarithmic nonlinearities and nonlocal terms. The analysis is based on two complementary operator decompositions. For the existence result, the equation is written as the sum of a principal Kirchhoff diffusion operator and a perturbation; the main part is treated via the Minty–Browder theorem while the remaining terms are handled through a Mawhin-type continuation degree argument. A second decomposition is then introduced to establish uniqueness by isolating a monotone component of the operator. This approach yields existence and uniqueness of weak solutions under assumptions weaker than those usually required in variational settings.