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<p>In this paper, we investigate the existence and concentration of solutions to a (<i>p</i>,&#xa0;<i>N</i>)-Laplace equation in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^N\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mi>N</mi> </msup> </math></EquationSource> </InlineEquation> involving a discontinuous nonlinearity and critical exponential growth. To establish the existence of solutions, we employ a penalization technique in the sense of Del Pino and Felmer adapted to a locally Lipschitz functional. Furthermore, by combining variational methods with Moser-type iteration techniques, we obtain the concentration behavior of the solutions. Our results contribute to the study of nonlinear elliptic problems with irregular nonlinearities and critical growth phenomena.</p>

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Concentration Phenomena for (p, N)-Laplace Equation Under Discontinuous Nonlinearities and Penalization Method

  • 期刊论文

  • 发表日期：

    2026年3月21日

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  • Ankit,
  • Giovany M. Figueiredo,
  • Abhishek Sarkar

摘要

In this paper, we investigate the existence and concentration of solutions to a (p, N)-Laplace equation in \(\mathbb {R}^N\) R N involving a discontinuous nonlinearity and critical exponential growth. To establish the existence of solutions, we employ a penalization technique in the sense of Del Pino and Felmer adapted to a locally Lipschitz functional. Furthermore, by combining variational methods with Moser-type iteration techniques, we obtain the concentration behavior of the solutions. Our results contribute to the study of nonlinear elliptic problems with irregular nonlinearities and critical growth phenomena.