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<p>In this paper we prove the existence of a signed ground state solution in the mountain pass level for a class of asymptotically linear elliptic problems, even when the nonlinearity is just continuous in the second variable. The (strongly) resonant and non-resonant cases are discussed under weaker conditions on the nonlinearity. A multiplicity result is also proved when <i>f</i> is odd with respect to the second variable.</p>

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A Nehari Approach for Asymptotically Linear Elliptic Problems

  • 期刊论文

  • 发表日期：

    2025年5月27日

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  • José R. S. Nascimento,
  • Marcos T. O. Pimenta,
  • João R. Santos Júnior

摘要

In this paper we prove the existence of a signed ground state solution in the mountain pass level for a class of asymptotically linear elliptic problems, even when the nonlinearity is just continuous in the second variable. The (strongly) resonant and non-resonant cases are discussed under weaker conditions on the nonlinearity. A multiplicity result is also proved when f is odd with respect to the second variable.