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<p>This paper is concerned with the study of solutions for a class of semilinear elliptic problem with dependence on the gradient when the nonlinear term satisfies a local Landesman–Lazer condition. The method used to establish the existence of solution combines the Lyapunov–Schmidt reduction method, minimax critical points theory and a fixed point theorem with appropriated truncation of the nonlinear term and an approximation argument. Results on the existence of multiple solutions are also provided. The results do not impose growth restriction at infinity on the nonlinear term and it may change sign.</p>

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Remarks on Semilinear Elliptic Problems with Dependence on the Gradient

  • 期刊论文

  • 发表日期：

    2025年5月9日

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  • M. C. M. Rezende,
  • P. M. Sánchez-Aguilar,
  • E. A. B. Silva

摘要

This paper is concerned with the study of solutions for a class of semilinear elliptic problem with dependence on the gradient when the nonlinear term satisfies a local Landesman–Lazer condition. The method used to establish the existence of solution combines the Lyapunov–Schmidt reduction method, minimax critical points theory and a fixed point theorem with appropriated truncation of the nonlinear term and an approximation argument. Results on the existence of multiple solutions are also provided. The results do not impose growth restriction at infinity on the nonlinear term and it may change sign.