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<p>In this work, we investigate the existence of at least three solutions to a variable exponent double-phase problem with a reaction term that is only locally Lipschitz continuous. Additionally, we analyse the sign properties of these solutions. Specifically, we establish the existence of two constant-sign solutions, one positive and one negative, using the Mountain Pass Theorem. The third solution, which is nodal (i.e., it changes sign), is obtained via the Nehari manifold approach. Finally, we demonstrate that the nodal solution has exactly two nodal domains.</p>

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Constant Sign and Nodal Solutions for Variable Exponent Double Phase Problem

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2025年6月28日

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  • Giuseppe Failla,
  • Leszek Gasiński,
  • Nikolaos S. Papageorgiou

摘要

In this work, we investigate the existence of at least three solutions to a variable exponent double-phase problem with a reaction term that is only locally Lipschitz continuous. Additionally, we analyse the sign properties of these solutions. Specifically, we establish the existence of two constant-sign solutions, one positive and one negative, using the Mountain Pass Theorem. The third solution, which is nodal (i.e., it changes sign), is obtained via the Nehari manifold approach. Finally, we demonstrate that the nodal solution has exactly two nodal domains.