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<p>In this work, we investigate a class of nonlinear boundary value problems within the framework of Sobolev spaces with variable exponents. After establishing precise formulations of these problems, we reformulate them as nonlinear hyperbolic-type equations. For each of the six problems considered, we establish both existence and uniqueness results. Furthermore, we address the associated stationary problems and prove the existence of solutions by applying a suitable variant of Brouwer’s fixed-point theorem.</p>

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On the Some Nonlinear Boundary Value Problems of Type Vibration in Sobolev Spaces with Variable Exponents

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • Fouzia Bouzeghaya,
  • Boubakeur Merouani

摘要

In this work, we investigate a class of nonlinear boundary value problems within the framework of Sobolev spaces with variable exponents. After establishing precise formulations of these problems, we reformulate them as nonlinear hyperbolic-type equations. For each of the six problems considered, we establish both existence and uniqueness results. Furthermore, we address the associated stationary problems and prove the existence of solutions by applying a suitable variant of Brouwer’s fixed-point theorem.